DIFFERENTIAL COST ACCOUNTING
DISSERTATION
Presented In Partial Fulfillment of the Requirements
for the Degree Doctor of Philosophy In the
Graduate School of the Ohio State
University
By
Paul LeMoyne Noble, B.S.C., M.B.A.
Tbs' Ohio State University
1952
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Table of Contents
ChaDter
2
1
Introduction
2
The Economic Background of Differential Costs
2?
3
The Relationship of Differential Cost to
Price
47
A Critique of Present Methods of Factory
Overhead Accounting and Control
72
5
Adapting Accounting Techniques to the
Differential Cost Approach
92
6
Non-manufacturing Uses of Differential
Cost Accounting
152
Conclusions
170
Appendix A
173
Appendix B
193
Bibliography
196
Autoblography
207
4
S210Q2
2
DIFFERENTIAL COST ACCOUNTING
Chapter 1
Introduction
Any treatment or discussion of the history of cost
accounting will readily point out and emphasize the rela­
tive recency of the development of the art.
It Is usually
recognized that accounting Is a young field In comparison
to the older professions of law and medicine, but general
financial accounting was well on Its way toward establish­
ment and recognition as a profession before much attention
was given to cost accounting.
It is generally recognized
that the modern age of accounting In this country had Its
roots In the huge Industrial and railroad expansion which
followed the Civil War.
This expansion caused the growth
of complex business structures resulting from combinations
and mergers which, in turn, gave rise to the need for
proper and adequate accounting.
Furthermore, this spec­
tacular expansion, particularly that of the railroads, was
financed to a considerable extent by capital from Great
Britain where the need for proper accounting methods had
already gained recognition.
British Investors, seeking to
protect their Investments, Insisted upon an accounting for
their American ventures $ and thus many accounting and
auditing techniques were Imported to this country.
By 188? the public accounting profession had devel­
oped to the point where a professional society was success­
fully formed, the American Association of Public Account­
ants.
Cost accounting at this time was just receiving the
first signs of attention.
Although some pioneers had in­
stalled factory cost systems as early at 1857*1 it was not
until the decade of the 1890's that; serious study was first
directed to costing.
2
It was not until 1919 that the
Rational Association of Cost Accountants was formed,
thirty-two years after the formation of the American
Association of Public Accountants.
In a body of knowledge so recently conceived, one
would hardly expect to find a clearly outlined set of
fundamental principles universally accepted through years
of testing and proven by successfully withstanding attack.
On the contrary, one would expect that the early years In
the development of a field of learning would be years of
trial and error and of searching for fundamental truths.
It is a period In which many hypotheses are advanced only
^"Mr. John W. Francis, In 18579 took charge of the
accounts of Bement A Dougherty, then well-known as manufac­
turers of machine tools and whose plant later became a part
of the Niles, Bement, Pond Co*,properties. In this position,
In addition to his regular duties, Mr. Francis undertook
the task of designing and installing a factory cost-system."
T, Edward Ross, PjEfrgers of Organised Public
. .9,
In Pennsylvania. 1942 p p
2 S. Paul Garner, "Historical Development of Cost
Accounting.M The
ting Review. October, 1947, Volume
XXII, pp.3o5-3o9.
to fall under the test of time and usefulness, while other
concepts must await full development pending the proper
background of circumstances.
Such have been the early years In the development of
the art of cost accounting, and It was In this setting that
differential costs had their beginnings.
All of these
early years might be described as the pioneer stage of cost
accounting, but Dr. Raymond P. Marpie, Assistant Secretary
of the National Association of Cost Accountants, conceives
of three distinct stages through which cost accounting
thinking has passed in these early years of Its develop­
ments first, what he terms the Inventory valuation and
profit measurement stage; secondly, the cost control stage;
and he feels that we are just entering upon the third, or
1
cost analysis stage. The concept of differential costs
was discussed In the very earliest years of the development
of cost accounting, 2 but the time and circumstances were
not ripe for Its full development and use.
It was not
until recently, when we entered upon the cost analysis
stage, that a full appreciation of the significance of
differential costs could be developed.
Dr. Marple states
It this ways "... during the early development of modern
1 Letter from Dr. Raymond P. Marple, dated July 23,
1951, addressed to the author, reproduced In full In
Appendix B.
2 Garner, op. clt., p. 389.
cost accounting— what I call the first stage or the
Inventory valuation and profit measurement stage— the need
for separate classification and treatment of fixed and
variable eosts was not appreciated or developed.
It was
not until we were well along In the second stage— the cost
control stage--that the development of* flexible budget
techniques forced recognition of the essential difference
between fixed and variable costs.
But it Is the third
stage, which we are just entering— the cost analysis stage—
which has brought home to a few cost accountants the way
In which this essential difference In the two types of
costs can be utilized to provide better cost Information,
not only for management policy determination, but for all
purposes for which costs are used."^"
Thus, the concept of differential cost Is not new— It
received mention In the earliest years of cost accounting,
but only recently have we begun to focus serious attention
upon the practical application of differential cost tech­
niques to managerial problems.
The first suggestion of the wide application of dif­
ferential costing appeared In an article by Jonathan Harris
2
In January, 1936.
In this article he proposed the
1 Ibid, Dr. Marple letter, Appendix B.
2 Harris, Jonathan, "What Did We Earn Last Month,n
Bulletin s t IMS national AffSPgAfftepfl, gf g&s.t
,
January, 1936, pp. 501-527*
■
elimination of fixed charges from inventories, which is
an approach to Inventory valuation based upon the dif1
ferentlal cost principle.
A storm of protesting letters
followed this proposal and were published In succeeding
Issues of the Bulletin of The National Association of Cost
Accountants.
However, the concept persisted and In succeed­
ing years it gained much momentum.
In the last several
years It has been the subject of a growing number of
articles In the N.A.C.A. Bulletin and has been discussed
at regional and national cost conferences.
It is the objective of this dissertation to test the
validity and reliability of the differential cost approach,
both from the theoretical and from the practical point of
view.
Economists have already Intensively studied the
theoretical aspects of the concept.
The present study
will review this theoretical background In an effort to
relate It to problems of accounting control as well as
test It In the light of practical observations.
After
thus establishing the theoretical basis for differential
costs, attention will be turned to the practical problems
of incorporating differential costs in the accounts,
reports and in accounting standards.
The theoretical aspects of the problem will be drawn
largely from the field of economics.
For practical ground­
ing, the problem was discussed with executives representing
1 SXt BP&fc* PP. 120 ff.
ten Industrial firms throughout Ohio.
Several of these
firms were chosen because It was known that they were
Interested in, or experimenting with, differential costs.
The remainder were chosen because of their willingness
to cooperate In the discussion of problems of accounting,
costing and pricing.
An abstract of these discussions Is
presented as Appendix A of this dissertation.
Before proceeding further, It would be well to
define differential costs.
Actually, differential costs
have wide applicability In many types of situations.
One
of the most common of these pertains to the production of
a firm In terms of units of product, and It Is In these
terms that differential costs are usually defined.
Blocker
says, "differential costs are the increase or decrease in
total costs that results from producing and distributing
additional or fewer units of product*"1
Thus assume a
firm Is now producing 50,000 units of product, which Is
something less than its full capacity, at a total cost of
$100,000, or an average total cost of $2 per unit.
Ob*
vlously some of the $100,000 Is fixed cost--that Is, cost
which does not necessarily change with changes In pro­
duction volume, while other costs Included In the total are
variable costs or those costs which are increased and de­
creased almost solely as the result of changes In
1 Blocker, John G.. CQ3&
McGraw-Hill Book Co., 1$487 p * tto.
New York*
8
production volume.
Let us further assume that of the
$100,000 total cost incurred, $30,000 may be classified as
fixed while the other $70,000, or $1.40 per unit, are var­
iable costs.
Given these existing conditions, it is now
proposed to produce an additional 10,000 units of product,
or 60,000 in all; and a question is raised as to the
cost of these 10,000 units.
We shall assume that no change
will occur in the fixed costs, and that a variable cost of
$1 •40 will be Incurred for each of the additional 10,000
units, as was Incurred for each of the previous 50,000
units.
One approach would calculate the cost of the 10,000
units as follows*
Fixed costs of the firm
$30,000
Variable costs (60,000 units @ $1.40 ea.)
Total cost of 60,000 units
Unit cost ($114,000 « 60,000)
Cost of 10,000 units <10,000 @ $1.90)
84.000
$114,000
$
1. 90 ea .
$ 19,000
This calculation and approach to cost determination is
referred to as the average total cost calculation, be­
cause it would average all the costs over
the units,
making no differentiation for the 10,000 new units as
distinguished from the 50,000 previous units being pro­
duced.
The differential cost approach would calculate the
cost of producing those 10,000 units as follows*
Present cost of producing 50,000 units
$100,000
Cost of producing 60.000 units (see
previous calculation above)
114-.OOQ
Additional cost Involved In producing
the added 10,000 units
Unit cost of each of the added
10,000 units
$
1.40
According to the differential cost approach, each added
unit costs $1.4-0, while according to the average total
cost approach, each of the 10,000 units costs $1.90.
There are several aspects of this simple definition
and Illustration which require further emphasis.
It
should be noted that differential costs are best under­
stood In comparison to total average costs; not only la
this true In defining differential costs, but It Is also
true In the application of the differential cost technique
to the solution of practical problems.
The average total
cost approach would insist upon spreading all costs equally
to all units, while the differential cost approach would
assign to any particular unit, or group of units, only
those costs arising directly as a result of the production
of those units.
These two approaches are not necessarily contra­
dictory; one Is not necessarily right and the other wrong,
but they do represent two different views of a set of
circumstances*
In th« field of general financial report­
ing, It Is becoming more and more recognized that there Is
not just one method of reporting, but rather that the form
and content of a financial report depends largely upon
the.use which is to be made of It.
The time Is coming
when cost accountants must recognize the same principle—
namely, that there Is not just one method of calculating
a cost, but the way In which a cost Is calculated should
depend largely upon the use to be made of It.
One of the
executives with whom this problem was discussed expressed
this view rather emphatically.
He said that in recent years
he has adopted a policy wherein he refused to submit cost
calculations for others in his organization until he knows
the purpose for .which the Information Is requested.
Thus both total costs and differential costs may
have their uses, but In the past the emphasis has, by
far, been placed upon total costs with less attention
being given to differential costs.
It Is one of the
objectives of this study to examine the relative signifi­
cance and Importance which has been assigned to the two
approaches and to determine whether the placing of the
emphasis should be reversed.
It Is further pointed out that the above definition
and illustration are greatly over-simplified.
In the first
place, It apparently assumes that the so-called variable
cost remains exactly constant at all levels of production;
that regardless of whether we are producing the first or
the thousandth or the sixty-thousandth unit, the variable
cost Is $1.40.
Practical conditions do not react In this
simplified way; although It Is called variable cost,
conditions usually are such that savings will be effected
In variable costs at certain volume levels, while In­
efficiencies will prevail at other volume levels.
Accord­
ingly, It may be somewhat inaccurate to use the $1.40 figure
at all levels of production, but this simplification does
not destroy the validity of the illustration.
Whether the
added cost of an additional unit of production is $1.40 or
$1.38 or $1*42 or even $2.00, it is this added cost which
constitutes the differential cost.
These fluctuations in
variable cost will also be the subject of further investi­
gation and analysis in this study.
Another over-simplification is found in the apparent
ease with which the total cost was classified into its
fixed and variable elements, and the ignoring altogether
of a semi-variable element.
The use of the classification
in the illustration is valid, but the actual segregation
of costs into these categories in practical circumstances
sometimes pose rather perplexing difficulties.
This
problem, as well as the problem of a semi-variable type
of cost, will also be examined in further detail.
The illustration further assumes the existence of
unused or idle plant capacity.
This is one of the more
common situations in which differential costs have been
used, but it is by no means the only situation.
The
differential cost of units of product may be calculated
at any volume level, even when operating at full or maxi­
mum capacity.
At such levels of operation, it may be found
that the differential cost of added units become exhorbitant because of Inefficiencies which enter into the pro­
ductive process; or the point will eventually be reached
where, in order to produce an added unit, additional
plant facilities must be acquired.
Thus, the amount of
the differential costs may vary widely, depending upon
the given circumstances of the situation.
The significant
point is that the approach can be applied at any level of
operation and is not limited to analyses of unused capacity,
although this is a common application of the technique.
Up to this point, the discussion has been entirely
in terms of the differential cost of added units of pro­
duction.
As stated earlier, this is one of the more common
uses of the differential cost technique; and most writers
have discussed differential costs almost solely in these
terms. Uhlle this is one area in which differential costs
can have great value, it is certainly not the only situa­
tion in which differential costs can be useful.
On the cone
trary, there is hardly a managerial decision in which
13
differential costs cannot be of use and Indeed may be
the very basis for managerial policy determination.
Several examples will help to demonstrate the wide
variety of circumstances in which the differential approach
can be utilized.
The possibility of plant expansion has
already been mentioned.
In a sense this might be classi­
fied as simply the problem of added units of production,
but the circumstances are sufficiently distinct as to
warrant separate consideration.
If, when discussing the building of a new plant, we
are thinking of the creation of an entirely new firm, we
may find that the differential, or variable cost, and the
total cost are exactly the same.
The distinction between
differential cost and total cost arises when we have some
existing fixed costs which may be spread over greater
activity without Increasing them In amount.
Thus,the
added or differential cost Is less than the total cost.
If an entirely new firm is created where there are no
previously existing fixed costs, then the differential
cost and the total cost of the new firm will be Identical.
Economists have stated this same concept In another
way— namely, that In the long run all costs are variable.
In other words, speaking In terms of extremely long
periods of time, we may think of firms coming and firms
going, the creation of firms and the discontinuance of
14
firms*
It is only when we ”slow down* our perspective
that we can begin to examine what goes on during the
life of a particular firm.
It is then that periodic
fluctuations in volume levels take on significance and
present pressing problems for objective study.
The distinction, then, between differential costs
and average total costs exists only in the short-run.
Thus, when we refer to differential cost applied to the
problem of the creation of additional plant facilities,
we are referring to the addition to the existing plant
through the creation of a new wing, a new building, or a
branch or subsidiary plant*
Under such conditions there are existing costs which
will not require extension in the operation of the new
plant— fixed costs which will remain essentially the
same.
In this circumstance, the number of variable costs
or differential costs will be much greater than in the case
of Increased utilization of existing plant facilities.
In
the latter situation, such costs as machinery depredation,
building depreciation, factory supervision and real estate
taxes are all fixed costs which would not Increase with
additional output.
In the event of constructing additional
plant facilities, all of these costs become variable.
Additional depredation costs would be Incurred for both
machinery and building, the services of additional factory
foremen and department heads would be acquired, new real
estate taxes would be levied on the new building, and many
other costs which are fixed with a given plant size would
now become variable.
However, not all costs would increase.
Many costs which were Incurred before the plant expansion
would continue with little change; for example, the cost
of salaries paid to the president and other key executives
and the expenses of the board of directors would not
necessarily change.
In other words the additional plant
facility might be operated with the same executive force,
at the same cost, as had previously been required.
The same
sales force might be utilized In the sale of the new out­
put with many fixed costs remaining essentially constant.
Thus, an average total cost calculation of the operations
of the added facility, based upon a full allocation of all
of the fixed costs, would be quite a different figure than
the differential cost.
This use of the differential cost technique Is a
variation of the basic problem of an Increase or decrease
in units of production.
There are many such variations
in problems which are fundamentally concerned with In­
creased or decreased production In which the differential
cost approach has great significance.
Such problems as
adding or discontinuing a product or line of products,
accepting a defense contract, opening a A#w territory ,or
16
discontinuing an old one, adopting a new channel of dis­
tribution such as a mail-order house— these are all var­
iations or the fundamental question of expanding or con­
tracting production and sales.
In every instance two
calculations could be made, one an average total cost
calculation, the other a differential cost calculation,
as demonstrated in the earlier Illustration.
In addition to questions Involving variations in
volume, the differential cost approach has value in a
wide variety of other matters calling for managerial
decisions.
As an illustration, let us assume that the
sales department reports that it could get a much higher
price for the product if it provided a one-year guarantee—
that the customers are requesting it and would be willing
to pay a higher price in order to obtain it.
We will
assume that the increase in selling price has been deter­
mined, and for the moment shall not concern ourselves
with that problem.
The question confronting us is the cost
of providing the guarantee, which can then be compared with
the added revenue which will be forthcoming.
The plan will
Involve estimating the number of returns of product to the
factory for repair during the first year after sale.
For
this purpose the company will set up a new "repair depart­
ment** within the present building*
Once again there are the same two approaches which
17
may be oaken In the calculation of the cost of this service,
as will be obvious from the Illustration presented In
Figure 1 on the following page.
Columns one and two reflect the traditional total
cost calculation In which a portion of all overhead costs
are allocated to the element being costed.
This tradi­
tional approach places a cost of $32,000 on the guarantee
proposal.
Column three, however, shows the total cost
of the plant operation before the adoption of the plan
and by comparing columns one and three, It is observed
that the total cost of operating the plant has Increased
by only $21,00d as a result of creating and operating the
repair department.
This Is the differential cost.
Column
five explains the difference of $11,000 In the two cost
calculations.
Which of these cost calculations carries
the most merit?
Which should be emphasized most by the
cost accountant and relied upon by management In deciding
whether or not to embark upon the guarantee plan?
Should
one approach be emphasized more than the other, or are they
of equal Importance?
These are questions whleh this study
will Investigate and try to answer.
This Illustration pertaining to the product guarantee
Is Intended to exemplify those circumstances wherein dif­
ferential cost Is of significance, aside from situations
pertaining to changes In units sold.
Actually there are
(1)
(2)
(3)
(4)
Budgeted
Difference
Cost of Plant Portion of
Between
Operations
Total
Plant Costs. Plant Costs
After
Cost
Before
Before
Adoption of
Allocated Adoption of
and
Guarantee
to Repair
Guarantee
After AdopPlan
Department
Plan
tion of Plan
Direct material (x units)
Direct labor (x units)
Factory overhead:
Salaries:
Plant Supervisor
Departmental Foremen
Indirect Labor
Building depreciation
Machinery depreciation
Taxes
Supplies
Repair parts
Totals
1100,000
100,000
*0*
$100,000
100,000
(5)
Differences
Between
Total Cost
and
Differential
Cost
Calculation
Col.2 - Col.4
mQn
—0“
•»Qbi;
15,000
20,000
40,000
50,000
50,000
10,000
10,000
5.000
$ 3,000
5,000
6,000
5,000
5,000
2,000
1,000
5*000
15,000
15,000
35,000
50,000
45,000
10,000
9,000
-0-
-0$ 5,000
5,000
-05,000
1,000
5.000
$ 3,000
-01,000
5,000
-02,000
™Q-0-
$400,000
$32,000
#379.000
$21,000
$11,000
Figure l.f Comparison of average total cost and differential
cost calculation of a specific proposal to provide a product
guarantee.
H
oa
<
19
many such decisions which confront management, all of which
may be approached from the differential cost point of view.
Such problems as producing a part or service previously
purchased, or discontinuing the production of a part or
service; providing additional services to customers, or
discontinuing such services; embarking upon an advertising
campaign or other promotional scheme; providing a service
or facility for employees or other employee promotional
schemes— all these and many other matters for managerial
policy determination require cost calculations*
Each
offers an opportunity for either the total or the differ­
ential cost approach, or both*
It Is significant that so many managerial decisions
provide an opportunity for development and use of differ­
ential costs; however, most of the literature on differen­
tial cost accoun&fcllg: overlooks or Ignores these many uses#
Writers have been prone to discuss differential costs
strictly in terms of increases or decreases In the units
of production, with little or no mention of the wealth of
other areas in which the analysis may be beneficial*1
Indeed, it Is difficult to visualize an Important manager­
ial decision without a differential cost aspect*
It is probably true, as,previously stated, that the
most common use of differential costs is in connection
with changes in volume.
1
Hence, this particular application
££• ante., Blocker, p* 7#
20
of* the technique will be used largely throughout this dis­
sertation when it is necessary to refer to examples and
illustrations; but It should be kept in mind that the
approach is equally applicable in a wide variety of* mana­
gerial policy circumstances.
Through the early years of the development of cost
accounting, a variety of cost concepts has been developed
with little uniformity of terminology.
Some of these con­
cepts and the terms used to describe them deal with essen­
tially the same idea as differential costs, and others bear
an Important relationship to differential costs.
It will
be fruitful to examine some of these in order to sharply
define their use.
Variable cost is a term we have already used In this
discussion.
In a very broad sense, variable cost may be
the same as differential cost— that is, we think of dif­
ferential costs as. those costs which will vary with changes
in production; therefore, they are Variable.
In a specific
i
sense and as commonly used, variable costs are usually
thought of as those costs which vary almost exactly pro­
portionately to production at all volume levels.
Thus,
material cost may be two dollars per unit at all volume
levels; hence, it is strictly a variable cost.
There are
other costs of this nature such as direct labor, power
and certain types of supplies, which vary in direct pro-
21
portion to production.
These are the costs which are
generally denoted by the term variable costs.
Such a
classification would strictly exclude any cost which does
not consistently vary with production, such as foremen
salaries, heat and light and other costs which are some­
times termed semi-variable*
Differential cost, while it would Include all of the
variable costs, might also include semi-variable costs
if additions to semi-variable costs were incurred as a
result of the differential action.
For example, it may be
proposed to produce an added 10,000 units of product; but
in order to do so, additional help must be provided in the
«
payroll department where the present work load has already
reached an absolute maximum.
The cost of the added payroll
clerk would be Included as a part of the differential cost
of added production, but is not what is normally considered
as variable cost since cost of the payroll department does
not vary directly in proportion to production*
The term variable has occasionally been used to denote
exactly the opposite concept of that referred to here—
namely, the costs which we have been calling fixed*
If one
thinks of the way in which costs behave in relation to one
unit, then it may be observed that the unit cost of such
items as real estate taxes will vary with the number of
units produced*
In other words if taxes in a particular
22
period amount to $1,000 and two units are produced, the unit
cost of taxes Is $500$ whereas if 10 units are produced,
the unit cost Is $100,
Thus, this cost varies with pro­
duction and Is termed a variable cost.
The term fixed cost has been used here to denote a
cost which remains fixed In total at varying output levels,
such as real estate taxes.
However, this term has also
been used occasionally to convey an opposite meaning.
Direct material cost, for example, may be $2 per unit for
every unit which Is produced; therefore, It Is fixed In
per unit amount.
Throughout this dissertation the term "variable" will
be used to denote those costs which vary In total amount
as production varies, and the term "fixed cost" will be
used to refer to those costs which do not change In total
amount as production varies.
Between those costs which are
purely variable and those which are completely fixed, there
are costs which are frequently referred to as semi-variable
or seml-flxed.
The Illustration given of the cost of pay­
roll Is an example.
In recent years, and for reasons which
will be developed later, there has been a tendency to
In­
clude these semi-variable costs In the term "fixed."1
In
a sense then, the term fixed Includes, broadly, two types
of costa— the semi-variable and the completely fixed.
The
latter are then sometimes referred to as "sunk costs,"
1 Lawrence, F.C. and Humphreys, E.N., wwyinsl Costing.
London: MacDonald & Evans, 194-7, p. 55.
23
shut-down costs,” "inescapeable costs” or "stand-by
costs.”
All these terms refer to an Identical concept—
namely, those costs which exist in the same amount, regard­
less of the level of production, such as building deprecia­
tion, top executives' salaries, real estate taxes and
insurance*
Direct cost is another term which has been used in
this general area of cost thinking.
However, the term has
not achieved altogether consistent usage.
Some writers
have used the term to imply the same meaning as "variable
cost" as it is used herein.
Quite recently, frequent
reference has been made to the "direct costing of inven­
tories."
Those using the term in this connection have
usually referred to a very loose and somewhat arbitrary
division of costs between differential and fixed.
This
problem is discussed in further detail in Chapter V.1
The term aatglfial cost is probably as nearly synony­
mous with differential cost as any of these terms.
This
is the term used by economists to express essentially the
same concept as that which has been defined herein as
differential cost.
One slight difference in the two terms
may lie in the fact that economists, in using the term
"marginal cost", usually think in terms of Increments of
0ne unit.
Differential costs, on the other hand, may
apply to any Increment, one unit or 10,000 units, as the
24particular situation may be.
It Is not uncommon today to
find accountants who usa the term "marginal cost" inter­
changeably with differential cost.
Incremental cost is a term which has had some usage
in the field of public utility accounting to express the
differential cost concept as It applies to units of output.
The term
cost expresses an idea quite
different from differential cost, but brief mention might
be appropriate in a summary of cost concepts.
This notion
views the cost of any particular thing in light of what
was foregone in order to produce it.
In other words, the
cost of any commodity amounts to the best alternative use
to which the factors of production, consumed in its
ufacture, could have been assigned.
man­
Thus, if the best
alternative use to which a given set of productive factors
could be used is in the production of consumer's goods
and these same factors are put to the production of machinery
then the cost of the consumer's goods is the amount of the
machinery which could otherwise be produced.
Attention to this cost concept has come almost entirely
from economists, where it has received considerable atten­
tion.
It has some rather Interesting implications pertain­
ing to accounting, but has received little attention from
accountants.
An examination of the opportunity cost as­
pects of accounting would provide fertile ground for
25
further examination.
A number of other terms which have a close relation­
ship to differential costs should be mentioned.
"out-of-pocket costs" is often mentioned.
The term
Sometimes It
has been used to refer to variable costs— that Is, those
costs which vary directly with production at all volume
levels.
At other times the term has been used to refer to
outlays for a specific proposal, and In this sense cor­
responds to differential cost.
Although descriptive, the
term has not been used consistently.
The term average total cost was used earlier to mean
a unit cost calculation which Includes all variable costs
Incurred In the unit's manufacture as well as a propor­
tionate share of all seoil-variable and fixed costs.
Another
term used to describe this concept Is full cost. These are
distinguished from unit differential costs,whlch refer
only to those costs incurred directly because of the man­
ufacture and sale of the unit.
As we shall see later, differential cost Is meaning­
ful primarily In relationship to differential revenue. By
this Is meant the gross addition to total revenue which
results from a particular action.
With respect to a par­
ticular action then, there Is the differential cost In­
curred and the differential revenue realised; and by
subtracting the cost from the revenue, there would remain
26
the net amount contributed by this action to the coverage
of fixed cost and the provision of net profit.
This con­
tribution may be referred to as differential profit.
27
Chapter 2
The Economic Background of Differential Costs
It would be difficult to determine specifically who
originated the differential cost concept.
Certainly the
concept Is an old one In economics where it Is more gen­
erally known as “marginal costs.'*
Economists usually trace
the marginal concept to the Austrian school of economics,
but most economists contend that men have been thinking
In terms of margins ever since the beginning of time.
The
Austrlans, however, are responsible for the term “margin*1
and were credited with consolidating thought with respect
to margins.1
The development of the concept as a tool of
economics resulted from the work of many economists In
succeeding years; but the one who probably contributed
most to relating marginal economics to practical business
problems was J. Maurice Clark In his book, eh titled
g tp flje jjf
s£
Qy.efftgftfl fig h ts .
2
The term “differential cost” Is used almost ex­
clusively In the field of accounting, and the concept was
probably developed by accountants Independent of the
marginal cost concept In economics.
This Is not
1 Gray, Alexander. Thq Development of Keonnm-te Doc­
trine . Londons Longman's Green and Company,1931, p. 330.
2 Clark, J. Maurice, Studies On the E e o n o n l o f
Overhead Costs. Chicago* Universityor Chicago, 19237
28
surprising In view of the observation that men have always
thought in terms of margins.
Nevertheless accountants have much to learn from
economists in this field, for economists have given much
study and development to the concept, while by comparison
it is only recently that accountants have begun to give
attention to the marginal Idea.
It might be fair to say
that the marginal idea has become one of the most Important
concepts in economic theory.
In economic analysis, it Is
one of the most important tools.
The marginal concept has been important In the analysis
of utility or satisfaction derived from economic goods, and
has received much attention In this connection.
However,
the marginal concept, as applied to costs and revenue, is
at the very core of the economist's analysis of the com*
plex functionings of business enterprises and markets.
Yet many cost accountants and most cost accounting text­
books, in dealing with the same problems and complexities,
have given it but slight attention.
To the economist, decisions to produce more or fewer
units of product, to expand productive facilities, to open
new territories— In fact, almost all business decisions
in the short run depend upon the relationship of marginal
cost to marginal revenue.
More specifically if the marginal
cost, or added cost, of producing an additional unit of
29
product Is less than the marginal or added revenue which
will result from the production, then It will obviously
be to the advantage of the firm to proceed with the pro­
duction of the unit.
For example, If the added cost of
producing another unit of product Is $1.40, whereas this
unit will add $1.80 to total revenue, the firm will gain
40£ by producing the unit regardless of the average total
cost.
M0nce the firm, under competitive conditions, obtains
a price per unit In excess of the variable cost per unit,
any further expansion of output Is profitable as long as
the additional cost per unit is less than the additional
receipts per unit.
When the two additional sums are equal
profits are at a maximum, or, under adverse conditions,
losses are at a minimum.
TJp to that point expansion of
output adds more to receipts than to costs and hence, con­
tributes to profit or to the reduction of any loss.
The
equality, then, of marginal costs and marginal receipts
when output is varied by one-unit changes indicates a
precise point of equilibrium for the firm.
This means
that, under the assumed conditions, the firm cannot Improve
its proflt-posltlon by altering output."1
This point of
equilibrium might be described as the Mpoint of maximum
1 James, Clifford L.. £fiSM|LLfi»> SftSlfi gZgblfflllg
Analysis. Hew Torks Prentlce-Hall, 1951, p. 128.
30
profit** since each unit of product up to this point adds
something to the total firm profit, whereas the next unit
beyond this point would incur a cost greater than its re­
venue and therefore detract from total firm profit*
Referring to the illustration in Chapter l,1 it will
be recalled that the differential or marginal cost of
producing the additional units was $1*40*
The total cost
calculation results in a cost of $1*90 each*
If the pro­
posed selling price of the additional units Is $1*80, It
can readily be seen that It Is a matter of some Importance
as to which of these cost figures should guide the firm In
arriving at a decision with respect to producing the added
units*
Most cost-accountants have emphasized the total
cost figure of $1*90, with attention being given to the
differential or marginal cost of $1*40; while economists,
In the short run at least, would regard the $1*40 as the
only significant figure*
It is true that In the long run,
2
economists would give consideration to total cost — this
will be given further consideration la ter .3 in the short
run, however, economists would contend that total cost Is
of relatively little significance In making decisions and
solving the day-by-day problems of business*
P* 9.
2 James, op. d t * , p. 193*
3 cf. post** p. 43*
31
As long as marginal cost Is lass than marginal revenue,
the desire to maximise profits will lead a firm to proceed
with the production and sale of the added unit.
But as
this production proceeds In accordance with these maxims,
a point Is reached where Inefficiencies start to develop;
and as a result marginal cost per unit will Increase.
Regardless of these Inefficiencies, It will still be de­
sirable to produce the added units as long as marginal cost
Is less than marginal revenue.
This will continue to be
desirable up to the point where marginal cost exactly equals
marginal revenue.
Thus, In the previous Illustration, the
next unit of product may require a differential outlay of
$1*50 and the next $1.60 and the next $1.75.
Yet, as long
as the selling price remains at $1.80, It Is beneficial to
produce the added units.
But If the next unit requires a
differential outlay of $1.85» with the selling priee re­
maining at $1.80, then It would obviously be foolhardy
to produce this unit.
Economists have expressed this basic
axiom In terms of a formula— namely, that mc=mr (marginal
eost In the short run must always equal marginal revenue).
Economists have placed this emphasis upon margins
because they believe that fundamentally people think In
terms of margins, and this point of view can be supported
by observations from every walk of life.
In view of this,
it is understandable that accountants and management are
32
Increasingly recognizing the Importance or the concept in
business decisions*
Although economists usually illustrate the application
or me=mr by rererence to units ot product, the concept is
basic to many situations involving managerial decisions.
In raet, it is clearly logical that any act contemplated
by management is desirable so long as the dirrerentlal
eost or the act is less than the dirrerentlal revenue
to be derived thererram*
Thus, the type or analysis Involved
in mc-mr is applicable to the many dirrerent examples outlined in Chapter 1,
appropriate*
1
where dirrerentlal cost analysis is
The question or adding a new product line,
opening a new territory, building a branch plant, adding
a new wing, or even embarking upon an advertising cam­
paign— in each Instance the decision hinges upon whether
or not the added revenue from the proposed action will be
greater than its dirrerentlal cost.
For illustration, rererenee is made to the illustratlon in Chapter 1,
2
wherein it was proposed to orrer a
one-year guarantee on the product and at the same time
increase the price.
It was stated at that time that we
would not concern ourselves with the amount or the price
increase, Tor at that time we were concerned with sheering
^ fifi-Altfl*♦ PP*
^ CXTa -flfltf.*y p* 18*
33
the way In which dirrerentlal cost was calculated as dis­
tinguished rrora total cost.
It will be recalled that In
this particular cast, It was determined that the dirrer­
entlal cost or the proposal was determined to be $21,000,
while the total cost was calculated at $32,000.
To con­
tinue the Illustration, let us assume that the sales de­
partment reports that the guarantee will provide an In­
crease sales revenue or $30,000.1
ir the cost accountant calculates the cost in accord­
ance with the total cost approach— namely, $32,000— It would
seem as though a $2,000 loss would result rrom the proposal*
The dirrerentlal cost approach, however, proves that the only
real cost Incurred In the guarantee Is $21,000;and If this
will result in $ 30,000 or added revenue, then the rirm
p p o n t will be $9 ,000 greater*
The essential considera­
tion In making management decisions Is the relationship
or dirrerentlal or marginal cost and dirrerentlal or
marginal revenue.
It is In this setting that the real
slgnirieance or dirrerentlal costs can be understood*
It Is quite obvious that dirrerentlal costs have
meaning only la relation to dirrerentlal revenue.
then, can the latter be calculated?
How,
The discussion has
^For purposes or simplicity, the Increase In sales
revenue Is assumed to result solely rrom Increased sell­
ing price, although the proposal might also create dir­
rerentlal revenue rrom Increased volume, or a decrease In
volume might orrset the Increase In revenue rrom the
Increased selling price*
■V
34
dealt at great length with the calculation of the differ­
ential cost, hut how can the $30,000 of added revenue be
determined in the preceding illustration?
While recogniz­
ing the Importance of this aspect of the problem, no at­
tempt will be made in this dissertation to solve the
practical problems which are involved.
This is clearly
a problem of market analysis and market research, and much
study and development is being carried on today in this
1
area.
Ho attempt shall be made here to infringe upon
what is rapidly becoming a highly specialized field of
market surveys.
Here it will merely be assumed that,
in one way or another, differential revenue can be esti­
mated; that, in the example cited, after diligent con­
sideration and study, $30,000 was the best possible
estimate of the revenue to be added from the proposed
course of action.
To those who might be skeptical of
such estimates, it is pointed out that management must
and does make these estimates before entering upon any
course of action.
The way of estimating may be crude or
it may be refined; it may consist of nothing more than the
president's best hunch, but nevertheless, there is an
estimate, and it is compared with differential cost
before a course of action is decided upon.
Undoubtedly,
the more study and effort which goes into the determination
1 Dean, Joel,
Hall, Inc., 1951 f
?Ty,f”1 Economics. New 7orks Prentlce-
35
of differential revenue, the oore reliable It will be;
but this is entirely a matter for the market analyst*
Although the practical aspects of estimating revenues
must be left to the market researchers, the economist has
contributed much toward an understanding of the theoretical
aspects of revenue behavior.
An understanding of these
theoretical aspects is essential to the full appreciation
of the Importance and uses of differential costs.
Broadly speaking, there are two ways In which the
revenue of firms may react to changes In volume.
The first
of these Is that situation wherein changes In the volume
of output of any one firm will have no effect whatever upon
the selling price of that output.
This does not necessar­
ily Imply that all of the conditions of the economic con­
cept of Mperfect competition" must be met; It Is just one
of many conditions found In the more competitive Indus1
tries. Mr. Howard Greer described this type of market as
peculiar to the "primary Industries'*, meaning those Indus­
tries dealing with raw materials close to their natural
source, as distinguished from "secondary Industries" which
fabricate the raw materials into an end product.
These
classifications merely use different terminology for what
the economist describes as first, a competitive market,
1 Greer, Howard C., In an unpublished address before
the Columbus Chapter of the National Association of Cost
Accountants, April 28, 1952, entitled "Accounting Aspects
of Business Policy Determination."
36
and secondly, a market or monopolistic competition.
In
the primary or competitive industries, the individual
firm has no control over price, there is great homogeneity
of product, and the volume of output of one firm has no
effect upon selling price.
Mr. Greer thinks in terms of
the primary industries because these conditions are more
likely to be found there.
Examples are to be found in the
great commodity markets, in the production of oil, timber,
minerals, etc., and even in the basic refinement of these
raw materials.
The products of each firm fall into several
classes, and beyond that are not distinguishable from the
product ©f any other firm in the Industry.
The price of
these products are determined in centralized markets
under conditions which tend toward perfect competition.
No one Individual firm has control over price.
Figure 2
on the following page Is illustrative of this type of
market situation, with each unit being disposed of at
$1.25 per unit regardless of the level of output.
With each Increment of output the differential revenue
remains the same, since this firm's output has no effect
upon the total market.
It will be noted that under these
assumed conditions the firm would continue to produce and
sell to a point a little beyond 120,000 units, for up to
this point differential cost is less than differential
revenue; but beyond this point the differential cost
Sales
Revenue
Production
None
• $1.25
Total
Cost
-o«
$4-0,000
48.000
Per Unit
10,000
$ 12,500
20,000
30,000
25,000
40.000
50.000
60.000
70,000
80,000
90,000
100,000
110,000
120,000
130,000
37.500
50.000
62.500
75.000
87,500
100,000
112,500
125.000
137.500
150.000
162.500
Unit
Total
Differential Differential Differential Average
Revenue
- Cost
Cost
Unit Cost
-O-
$12,500
55.000
61,000
68,000
12,500
12,500
75.000
12.500
12,500
82.000
90,000
99,600
109,000
120,000
131,000
143.000
156.000
12.500
12.500
12.500
12,500
12,500
12,500
12.500
12.500
-O8,000
7,000
6,000
7,000
7.000
7.000
8,000
9,000
10,000
11,000
11,000
12,000
13,000
-o.80
.70
.60
.70
.70
.70
.80
.90
1.00
- 0-
$4.8000
2.7500
2.0333
1.7000
1.5000
1.3667
1.2855
1.2375
1.2111
1.10
1.2000
1.10
1.20
1.1909
1.1917
1.30
1.2000
Figure 2. Example of changing output and changing costs with constant
revenue per unit of product.
UJ
si
($13*000) is more than differential revenue ($12,500).
The second type of market-*that which economists term
monopolistic competition— is what Mr. Greer described as
typical of secondary industries, the main feature being
that here the firm has some control over the selling price
of its product.
Economists have gone on to describe this
type of market as one in which the product of each firm is
different from that of any other firm in the industry.
This differentiation may be slight, such as insignificant
variations in style or size or color, or the difference
may only be in wrapping (example, bread, cigarettes, etc.)
or in a trademark or label.
Nevertheless, the difference
is sufficient that customers build up a preference for a
particular brand and are willing to insist upon this brand
within a certain range of price fluctuations.
Economists
express this situation as one in which there Is a separate
"demand curve" for the product of each firm in the industry,
rather than one "demand curve" applicable to the entire
industry.
In other words, the firm may raise or lower the
price of its particular product with corresponding fluctua­
tions in the demand for its product.
Figure 3, on the
following page, is illustrative.
It is observed that in order to Increase sales from
600,000 to 700,000 units, it is necessary to reduce the
unit selling price from 93£ to 92£.
Thus, the added or
Sales
and
Production
_ Units
Selling Price
Necessary
To Dispose Of
Production
Sales
Revenue At
Indicated
Price
Total
_ Cos t
Differential
Revenue
Differential
Cost
-0-
-0-
600,000
*.93
*558,000
*558,000
700,000
.92
644,000
567,000
*86,000
800,000
.90
720,000
600,000
7$,ooo
33,000
900,000
.88
792,000
657,000
72,000
57,000
1,000,000
.86
860,000
720,000
68,000
63,000
1,100,000
• 82
902,000
795,000
42,000
75,000
1,200,000
.78
936,000
936,000
34,000
122,500
Figure 3. Example of changing output and costs with changing revenue
per unit of product.
$
9,000
40
differential revenue is Increased not by 100,000 X 93*,
nor even 100,000 X 92*, but the increase is as followss
100,000 units X 92*
=
$92,000
Less 600,000 units reduced 1*
■
6.000
Net Increase in revenue
$ 86,000
Although proposals for changes in volume must now
consider a new unit selling price, the application of the
rule of me*mr is just as valid here as in the previous
type of market.
Specifically, this firm would produce
slightly more than 1,000,000 units, but would not go to
1,100,000.
Up to the 1,000,000 unit level, the differential
cost of each Increment is less than the differential revenue,
but the cost of producing the next 100,000 units ($75,000)
is considerably more than the addition to revenue ($42,000).
A further possibility exists with respect to this
monopolistic competition type of market— namely, that it
may be possible to maintain the existing market, with its
existing level of output and existing selling price, and
to sell the new output In a new and separate market without
affecting the old market.
In Figure 3 it is seen that
the firm will stop producing at the 1,000,000 unit level
since the next 100,000 units would reduce overall selling
price to eighty*two cents and the increase in total
revenue would be only $42,000, whereas the added cost of
41
these units would be $75*OOO.
But what would the situation
be If the firm could maintain the sale of the existing
1,000,000 units at eighty-six cents and, by entering a
new market, dispose of another 100,000 units at elghtytwo cents?
Total revenue from the 1,100,000 units would
consist of 1,000,000 at elghty-slx cents or $860,000 and
100.000 units at eighty-four cents or $84,000 or total
revenue of $944,000.
All of the revenue from the added
output comprises differential revenue, or $84,000, while
differential cost remains the same--namely, $75,000; and
under these circumstances since me Is less than mr, It
would now be beneficial to Increase production to the
1.100.000 level.
This type of analysis is not new to economists.1
Furthermore, there Is ample evidence that management uses
this technique whenever the opportunity Is present.
Many examples can be cited of areas In which this technique
may be applied.
A new territory may be opened up In a
neighboring state or sale of the additional product at
a reduced price may be accomplished through a mail-order
house.
In either of these Instances the additional
product will probably be marketed under a different brand
name so that It will not be directly related to the
marketing of the old product.
1 Dean,
op.
clt., p. 512.
42
Another variation of this same procedure Is found In
the bidding on governmental or defense contracts to pro­
duce and sell a product at a price lower than that of the
product sold In the civilian market.
Another procedure
has been to enter the foreign market at a reduced price,
this being so completely separated from the domestic mar­
ket that It will have no effect upon the latter.
One of
the executives Interviewed In this study made the obser­
vation that his firm has entered the foreign market at a
consistent price reduction of ±0% below selling price In
this country.
All of these methods are a means of tapping
additional markets, without disturbing conditions In the
existing markets or maximizing the excess of differential
revenue over differential cost.
From the viewpoint of the
economist, this creates a new product In a new market,
with a demand curve distinct from that of the old product.
There Is one further consideration with respect to
entering new markets at lowered prices to obtain a differ­
ential revenue advantage.
In discussions with one
executive, he was quick to point out that competitors
may look upon such action as "p*lee cutting** and retalia­
tory action may lead eventually to price wars.
This serves
to emphasize that budgeting or estimating differential
revenue Is not an easy task.
Careful and complete market
analyses must be conducted, considering the total effect
43
or the proposed action, including the reaction of competi­
tors •
Up to this point, all of the discussion in this
chapter has pertained to the economists1 analysis of mar­
ginal or differential, cost and their application to ac­
counting problems.
What of the economists' total cost?
So far, little or no mention has been made of this.
Is
total cost of little significance in economic analysis?
Quite to the contrary, total cost has an Important role In
economic analysis, but Its significance Is found mainly
in the economists' long run concept.
Economic ^analysis has placed much emphasis upon the
distinction between the short run and the 16ng run.
Economists have recognised that In the study and under­
standing of economic phenomena this distinction must be
observed, that certain things are true In the short run
while others are true In the long run.
Total cost, in relation to prices and managerial
decisions, has significance to the economist primarily
in the long run; it is of lesser significance In the
day-to-day decisions with respect to production and sales.
As has been demonstrated, these problems are marginal cost
problems; and these are considered economically as short
run concepts.
In the long run, economists recognise that total
revenue must be sufficient to cover total
cob
t.
If this
were not true In the long run, firms would seek other more
profitable outlets for their capital Investments and leave
the industry In which revenue Is not sufficient to cover
cost.
The threat of this would force prices to rise In
the Industry to a point sufficient to attract and main­
tain sufficient capital.
This In essence is the role of
total cost In economic analysis.
But In their day-te-day
decisions, management cannot leave the Industry one day,
If prices aren't right, and go back in the next day.
The
costs of productive facilities as well as other fixed costs
have been "sunk" in the firm.
The most that management
can do In Its day-to-day operations Is to make certain
that added or differential outlays are at least covered
by revenue, and also to max-tmi
the extent to which this
revenue exceeds differential cost.
Economists have made much of the distinction between
long run and short run, while accountants seldom make any
such distinction.
The accounting method for determination
of costs and profits in the past has corresponded very
cosely to the economists long run concept.
The accountant
in computing Income has usually taken Into consideration
the long run life of the enterprise as a basis for his
costing.
Many costs, entering Into Inventory values for
the balance sheet and for the Income statement, have been
45
computed as though the accountant were standing at some
distance viewing the entire life of the firm.
Examples
are found In the depreciation of facilities for long periods
of time, and the proration of fixed costs over all units
of production so as to compute a long run average total
cost figure.
Accountants have been long run minded even to the
point of Ignoring the existence of the economic concept of
the short run.
Management Is supplied by the accountant
with long run average total cost figures for the solution
of short run day-to-day problems.
As has been pointed out,
differential cost accounting or what might be termed shortrun accounting, offers the solution to these day-to-day
problems•
What Is needed Is a general recognition, In practice
as well as theory, of a short run and a long run accounting
concept In much the same way that this distinction exists
In economics.
Accountants readily recognise that they are
dealing with economic problems and economic matters, and
it would therefore seem logical to assume that the two fields
would be dealing with essentially the same concepts.
many instances, however, this Is not true.
In
Economists
could benefit from the accountants' practical Insight
Into many matters.
On the other hand, economists have
made thorough study of Important matters which have escaped
the attention of accountants, such as this distinction
between the long run and short run.
A much closer study
by each group or the work of the other would certainly
prove to be mutually beneficial.
Chapter 3
The Relationship of Differential Cost to Price
Those who object to the use of differential unit
costs usually do so on the basis of the assertion that a
knowledge of average total costs Is vital for proper price
setting.
They claim that unit total cost must be con­
sidered in price setting In order to insure the avoidance
of loss.
This Is an Interesting view for a number of reasons.
First, it Is interesting because some business executives
support the view while others just as strongly deny that
average total cost per unit has anything to do with price
setting.
Secondly, It Is interesting because it Is re­
lated to very extensive studies which economists have
made In this area of price determination.
First, a brief summary of the economists' thinking on
this subject.
From a purely theoretical point of view, It
has been shown that In the short run, price Is determined
by the operation of the forces of supply and demand.
Many
factors may influence supply and demand; but In the final
analysis, these are theoretically the determinants.
With
price In the short run being determined Independently of
cost, a firm then strives to equate
cost and
marginal revenue in the manner described In Chapter 2.
It should be noted that marginal cost does not determine
price.
Price Is Independly established by the functioning
48
of supply and demand, and then the firm makes Its decision
to produce or not to produce on the basis of marginal
cost and marginal revenue.
All this Is first established as the theoretical
functioning of price determination, but economists have
been quick to emphasize that In practice, price determina­
tion usually does not work In this manner.
Many economists
have concluded that In practice, prices are determined
largely by the calculation of an average total unit cost
to which Is added a mark-up for profit.
Professor Clifford
L. James makes mention of this approach to price setting
In his textbook
and analyzes the problem further In his
course In Intermediate
2
Analysis.
presses this viewpoint when he says*
John l>ue ex­
"The need for a
feasible approach to pricing In a multipie-product situation,
plus the desire to avoid the price Instability which the
existence of common costs creates, and the desire— ever
present In oligopoly— to lessen uncertainty and attain more
closely the maximum joint-profit price level have resulted
In the development In many Industries of a technique of
price-setting which employs average cost rather than
1
James, Clifford L.« Economics Basle Probiaap
An«Will». Hew Yorks Prentlee-Hall, Inc., 1951, p. 124.
2 From lectures by Professor Clifford L. James In
Yiffi1T t Ohio State
49
i
marginal coat.
Essentially, this method Involves the use
as the basis for price-setting of an estimated average-cost
figure, which Includes a share of common cost allocated to
1
the various products on some selected basis*"
Although many economists have concurred In this
explanation of price determination, two English economists
are usually credited with first developing this thesis.
R. L. Hall and C. J* Hitch, writing In 1939, said*
"The
purpose of this paper Is to examine, In the light of the
Interviews, the way In which businessmen decide what price
to charge for their products and what output to produce.
It casts doubt on the general applicability of the conven­
tional analysis of price and output policy In terms of
marginal cost and marginal revenue and suggests a mode of
entrepreneurial behaviour which current economic doctrine
tends to Ignore*
This is the basing of price upon what we
shall call the 'full cost' principle, to be explained In
detail below*
More recently a study was conducted by The National
Bureau of Economic Research regarding the practical methods
of determining,price*
It recognized that price setting
was extremely complex, and It devoted much time to a dis­
cussion of varying practices In different firms*
However,
1
?ob?
BMHSKlS Analysis.
Chicago} Richard D. Irwin, 1950, p. 293*
V.
2 Hall, R.L. and Hitch, C.J., Prlc* Theory and
B»h»vlor. <&£ax& Bcononlc P a w . £ 2* £, HCjr 1939, p. 12.
5o
the general reeling seemed to be that most practices were
a variation of the total-cost-plus-a-mark-up technique.
This study concluded that one of the primary reasons that
executives did not think in terms of margins was because
they could not determine margins— not only marginal costs
but more particularly marginal revenue was not known.
It
was contended that businessmen were not familiar with
either their marginal cost or marginal revenue figures.1
A number of the firms studied in this dissertation
confirmed the view that prices were based upon average
total unit costs.
One officer asserted that the only
justification for the existence of the cost department
was to supply information to the sales department for price
setting purposes.
When asked what kind of cost information
he presented to the sales department, he replied ntotal
unit costs".
An official in another company explained that in their
firm, costs were calculated only every six months.
This
was a firm that manufactured about fifty different items
in a coordinated line, and the cost calculation was full,
historical allocation of total costs to all products in
the line.
Suspecting that such an infrequent cost cal­
culation could hardly be of use for cost control purposes,
'
•
\
a question was asked as to the purpose of this semi-annual
1Cost Bahavio^ and Prlee Policy - New Yorks National
Bureau or Economic Besearch, 19*3*
51
cost calculation.
This answer was an unequivocal "for
price setting purposes.**
The experiences of these firms would seem to support
the views of the economists quoted above.
However, this
i
viewpoint was not by any means found to be unanimous.
In
fact, just the opposite attitude prevailed with some
executives.
They felt that average total unit cost had
no particular relation to selling prices.
Their views of
price determination corresponded roughly to the theoretical
propositions outlined above--that price was determined
Independent of total unit cost In the short-run, and
that the decision to enter or not to enter the market at
the established price was essentially a matter of dif­
ferential cost In relation to differential revenue.
One of the strong supporters of this point of view Is
Hr. Howard C. Greer.
He developed this subject extensively
In a talk given before the Columbus Chapter of the National
Association of Cost Accountants on April 28, 1952.
He
made the assertion that It Is a complete fallacy to think
that eosts should or do determine selling price.
Mr. Greer
would Insist that price In the market Is determined
Independent of cost.
Logic and reasonableness would appear to support Mr.
Greer's view.
What Is there In a cost accountant's total
cost figure which would determine the value of a product
In terms of the amount which a consumer would he willing
to pay for it?
There are first, the direct costs of pro­
ducing the particular unit— materials, productive labor,
etc.
If these were the only costs to be considered, would
the consumers* willingness to pay follow In proportion to
these costs?
We are all familiar with examples of products
which obviously have small material and labor cost, but
which demand a sizable price due to their novelty or other
peculiar circumstances.
The arbitrary proratlon of Indirect costs adds further
difficulty In determining a total cost figure.
There are
admittedly a variety of bases upon which many Indirect
overhead costs may be allocated to products.
Is It
reasonable for management to think that selling price should
logically conform to the arbitrary method by which the
cost accountant chooses to prorate these eosts?
Is the
degree of desire on the part of a consumer affected by
cost allocations?
Revenue from all products combined
should, It Is true, cover total Indirect and fixed costs
of the firm.
Yet one particular product In the group may
have great saleability and hence command a. high price,
while another may have only slight saleability and hence
command a lower price.
Yet, In spite of these facts, a
logical treatment of Indirect cost might allocate Iden­
tical amounts to each product.
53
It does not seem reasonable to expect that consumers
would necessarily pay a price based upon an arbitrary cost
calculation or any cost for that matter.
Price does not
guarantee cost recovery except perhaps in that Instance
where the seller is in a monopoly position.
If there is
no other source of supply for the product, it is con­
ceivable that the moncpolist could dictate a price and
maintain it, adjusting n-: output to the point on the
demand curve which corresponds to this price*
Further understanding of this perplexing problem
may be gained by raising a question as to what a total
cost figure indicates with respect to price*
Suppose
that the cost accountant makes a complete allocation of all
costs to products, and on this basis certain products show
net losses*
Refer, for example, to the illustration used
in Chapter l1 wherein a total unit cost calculation resulted
in a cost of $1*90 per unit, with a selling price of $1*80*
What should now be done with respect to such a loss product?
Assuming that all possibilities of cost reduction have
been exhausted, is the solution to be found in discon­
tinuing tills product?
It will be recalled that in the
above Illustration, the units which had a total cost of
$1*90 had a differential cost of only $1*4-0*
Since the
units are contributing some thing to the coverage of the
firm's fixed cost, the firm would obviously lose 4-01 per
unit by discontinuing this production and sale.
S&t
P- 8 .
Clearly
54
the answer here Is to he found In the differential ap­
proach.
It Is not the total cost which throws any light on
the situation; hut rather, since the differential cost
of producing the product Is slightly less than the revenue
which It adds to the total, then the production and sale
of the product Is contributing 40£ to covering the firm's
pool of fixed costs.
In such a circumstance, the firm Is
better off by continuing the production and sale of the
product than If It were to discontinue It.
For completeness It should be pointed out that In a
circumstance of this kind another possibility exists.
It
may be found that the productive facilities which are being
devoted to the "loss* product could better be devoted to
some other product.
This would be governed by a determi­
nation of whether an alternative product would contribute
more to the covering of the fixed pool of costs than Is
the present product.
In other words, Is the excess of the
differential revenue over the differential cost of the
alternative product greater than It Is In the ease of the
product currently being produced?
This discussion, although It utilizes the marginal
cost approach, is really a problem of opportunity or
alternative costs which was discussed briefly In Chapter
I.1
It Is a problem which exists In any Instance ’L
> p* 24*
where maximum capacity Is being utilised; management is
constantly faced with the questions could these facilities
be devoted to a more profitable use?
This was brought out
in a discussion with one executive who cited an example
of a product, the selling price of which did not cover
total cost (he had no specific knowledge of differential
cost).
However, the production of this product was tying
up facilities and using valuable space which could better
be devoted to other uses.
This was in a period of high
plant activity, thus space was at a premium and a question
of best alternative use of plant facilities was pressing.
If a plant is producing at less than full capacity
and idle.facilities exist, the problem of alternatives
becomes one of choice of products to utilize the Idle
facilities.
That product which will produce the great­
est differential profit should be added to production to
contribute what it can to the coverage of the fixed costs
of the firm.
Even in these circumstances, however, another kind of
alternative still presents Itself— that is, the alternative
of selling the firh or;liquidation and dissolution.
It
is a question of the best disposition of the assets of the
firm— should they be used to produce product A and B, or
one and not the other if facilities are not sufficient
for both; or should the facilities be sold and the firm
56
dissolved?
The alternative is always present that the
best alternative disposition of the firm's productive
facilities is to sell them*
In summary then, it may be said that loss based upon
total cost is not conclusive evidence that the production
of a product should be discontinued.
Rather, if the prod­
uct is providing some differential profit, its continued
production is desirable subject to the best alternative
use of the facilities now devoted to its manufacture*
Returning to the Illustration in which a total cost
allocation to products resulted in a loss for certain
products, it has been shown that discontinuance of the
production of the "loss” products is primarily a matter
of differential cost and not total cost per unit.
Inves­
tigating further, they readily admitted that they recog­
nized that it was desirable to continue to produce the
article for what it would contribute to the coverage of
fixed overhead*
Although this was recognized in prin­
ciple, in most instances these executives had no accurate
knowledge of how far selling price could fall before it
would no longer contribute something to the coverage of the
firm's pool of fixed costs*
One executive "guessed** that
he could decrease selling price below total cost by "about
15$ of his total overhead costs*"
Others knew that they
might still produce and sell with selling price below
57
total cost, but didn't know how much below.
There would appear to be another possible approach
In that situation In which a total cost allocation to
products has been made and has resulted In loss for cer­
tain products.
If It Is not desirable to discontinue
the manufacture and sale of the product, then why not
increase the selling price?
As was pointed out above,
there Is ample evidence In some firms that price determined
by total cost Is being used quite successfully.
The execu­
tive of one firm, upon questioning, estimated that In 85%
of his products, selling price determined upon the basis
of average total cost plus a mark-up Is the final selling
price.
In only 1.5% of the cases Is further adjustment
necessary as he stated, "to meet competition.n
If one has such control over his selling price so as
to raise and lower it at will, It Is quite obvious that the
market Is something less than purely competitive.
Some
degree of monopoly must exist in order to be able to
raise the selling price when arbitrary total cost alloca­
tions Indicate a "loss".
In more competitive markets
the producer has no such opportunity to manipulate his
selling price.
In summary, It has been pointed out that first,
average total cost calculations are highly arbitrary and
cannot consistently form a basis for consumer values as
58
expressed In a competitively determined price.
Only the
arbitrary cost calculation of a monopolist could bedome
the basis for a price and then maintain It.
Secondly,
products which show "losses" based upon total cost
allocations should not necessarily be discontinued.
Here Is a differential cost matter.
These observations appear to lead to the conclusion
that average total unit cost calculations have little
value In a competitive market, but that as a smaller
degree of competition exists, more use ean be made of
average total costs.
Inversely there is a direct relation­
ship between the degree of competition which exists and
the Importance of differential costs In executive policy
determination.
This hypothesis appears to be the answer to the
seeming paradox which exists between the points of view
expressed earlier* (1) price Is determined largely by
average total unit costs; (2) price is determined Inde­
pendent of total cost, but the decision to enter or not
to enter the market rests upon differential cost and
differential revenue.
Those who support the second
position are apparently basing their observations upon more
competitive types of industries, where average total costs
have been of less significance.
Economists, on the other
hand, do stress the lack of competition In Industry and
59
have placed considerable emphasis upon monopolistic elements
wherever they have been found.
If the above hypothesis
Is true, that total unit costs are of value where compe­
tition Is slight, then It Is understandable that economists
should observe their use In studying monopolistic situations*
Since this postulate appeared so valid In theory, It
was the subject of questioning and further examination in
the firms visited; and In each Instance the facts bore
out the truth of the theory in a very clear manner*
In each of the firms, the executive being Interviewed
was asked whether he considered that he was faced with
keen competition in his business*
In all but one Instance,
the answer was in the affirmative but with varying degrees
of emphasis*
In the one firm which admitted that It had no really
close competitors, there was without a doubt the most
resistance to the Idea of differential costs*
First, the
executives had practically no notion of the meaning of
differential costs or marginal costs.
Upon development
of the Idea, they seemed mildly Interested but Insisted
that their average total cost calculations were of para­
mount Importance.
This was the firm ugfclch developed actual,
historical average total unit costs of each product every
six months.
This semi-annual calculation followed the
usual pattern, with elaborate schemes for apportioning
all fixed and Indirect costs to products.
These execu­
tives were convinced that they were doing an unusually
good job of making these prorations, and this was respon­
sible for their ability to develop correct prices.
Fur­
thermore, they felt that these careful total cost calcu­
lations were largely responsible for the fact that they
had quite successfully "avoided inviting competition.’•
They felt that they were producing the product very effi­
ciently and that careful average total cost calculations,
plus a "modest1* mark-up for profit, would yield a selling
price which was fair and which would be difficult for a
competitor to meet.
In their opinion, as a result of this
policy, they had been quite successful in discouraging
competition.
Another Instance similar to this was observed some
years ago,
not in connection with this present study.
This took place in a company which manufactured basically
a single, highly specialized product in several sizes and
varieties.
In this instance the company auditors, In
conjunction with their year-end audit, were asked to make
a calculation of the cost of manufacture and sale $£ each
variety and size of product produced.
The usual pro­
cedures for cost calculation were employed, with fixed costs
1 Based upon observations of the author during several
years of public accounting practice as a staff member of
the firm of Haskins & Sells, Certified Public Accountants,
Cleveland, Ohio*
prorated upon what appeared to the auditors to he the beat
basis available.
To these total cost calculations was
added a mark-up for profit, and this became without ex­
ception the list price for the following year..
This firm
can be described as very successful, but the top executive
of the firm admitted they had practically no competition.
They were, at that time, the only manufacturer of this
particular product.
It Was marketed over a wide area
comprising a large number of states.
In other areas this
firm licensed its patented processes to another concern
for the manufacture and distribution of the product.
The support of the basic hypothesis— that there is a
direct relationship between the degree of competition
and the importance of differential cost information— was
just as clearly demonstrated at the opposite extreme,
where a high degree of competition exists.
Ur. Greer's experience comes largely from Industries
which are highly competitive— the meat packing Industry
and the railroad Industry (competing with motor trucks).
From both fields he cited numerous examples of the appli­
cation of the differential cost technique.
In the meat
packing industry he was with one of the smaller companies,
competing with the meat packing glants— Swlft, Armour, etc.—
for a small share of the market.
Although the railroads
are not competitive in the sense of being in direct
62
competition with each other and freight rates are under
the control of the Interstate Commerce Commission, yet the
railroad with which Mr. Greer was connected felt very
keenly the competition for freight traffic from the motor
trucking Industry.
The executives constantly had to con­
sider the pressure from motor trucking rates and service*
So Mr. Greer*s whole outlook Is one of keen competition
i
and correspondingly one of differential cost analysis.
In 1944-, addressing the 25th Annual International Cost
Conference In Chicago, Mr. Greer salds
"When the cost
accountant can talk as glibly about the marginal cost of
any given Job or lot of product as he now does about
scientific methods of overhead allocation, he can help to
solve one of the problems which will be most pressing in
the postwar era."'1'
Other business executives faced with keen competition
were most appreciative of differential costs.
The sharp
clash between the differential approach and the traditional
total cost approach was clearly outlined In one of the
finis which handled a low priced? highly competitive
specialty Item.
This product Is marketed through drug
stores where It Is usually displayed beside the products of
Its competitors.
The executive Interviewed In this firm
1 Greer, Howard C«, "Cost Requirements of a Competi­
tive Economy", The nation*! Association of Cost AS£gSR£~
frAtot Twenty-fifth International Cost Conference,.
Chicago, 111., 1944, p. 122.
63
was not an accounting executive, but was associated with the
production or the product.
Nevertheless,he had a clear
appreciation or the need ror differential cost Information.
He had long relt the shortcomings or the traditional total
cost InTormatlon which was supplied to him by the cost
accounting department, and is now In the process or ex­
perimenting with the dirferentlal cost approach.
He
reports that the approach is already providing much
valuable Cost InTormatlon Tor effective control and
guidance or the business.
Between these extremes, admitted monopoly on the one
hand and keen competition on the other, are the other
Tlrms studied which might be classlTled at varying degrees
in between.
Even In these cases where the distinction
between competition and monopoly was not quite so marked,
the extent or degree oT competition seemed to Tollmr
closely the rirms? Interest In and reliance upon dlTTerentlal costs.
Some oT the Tlrms studies were engaged in the manuTacture oT heavy, high unit value, Industrial machinery.
From all appearances they seemed to be In much the same
position with respect to conditions oT production, sales,
competition, etc.
Upon closer analysis, It developed that
two oT these Tlrms were vitally interested in dlTTerentlal
costs,while In a third there was only mild Interest In the
subject.
Further Inquiry developed the fact that the
business of the first two was highly competitive.
The
price charged for their products was strictly a competitive
price and bore no particular relationship to total unit
costs.
The third firm was the one In which the statement
was made that price was determined as total cost plus a
percentage.
The price so determined remained unchanged In
85JC of the cases.
In the remaining 15£ of the products,
some variation In selling price was necessary in order
"to meet competition" •
This would seem to indicate that
In the other &5% of the cases, competition was not strong
enough to force fluctuation In price from the one based
upon an arbitrary total cost.
There was one Interesting feature In these companies,
all producing heavy industrial machinery, which may account
for the greater degree of competition In the first two than
In the third.
Sales In the first two were largely a "one­
time" proposition.
There was little repeat business re­
sulting from customer goodwill, etc.
In the third company,
however, repeat business was an Important factor.
The
product was such that frequent repairs were required and
machines wore out rather rapidly.
Consequently the firm
had succeeded In building up a large customer following.
Companies which had for years bought their machinery from
this same firm depended upon It for service and replace­
ments.
65
There were other manufacturers of the same kind of
machinery, but their competition was slight.
Fundamentally
It was a condition of monopolistic competition resulting
almost solely from a "repeat-business” type of Industry.
All of the cases studied seem to point toward correla­
tion between the degree of competition and the appreciation
and use of differential costs.
Conversely it may be said
that where monopolistic tendencies are present, there Is
less use or comprehension of differential costs and great­
er emphasis upon total unit costs.
This theory and the observation of its practical
applications are entirely consistent with the Ideas ad­
vanced In Chapter 2.
There It was developed that average
total unit costs were an exemplification of the economists
long run.
Now It Is shown that average total unit costs
are highly regarded as a guide to price setting where
there is a lack of keen competition.
perfectly compatible.
These two views are
A firm in a monopollstkposltlon
might take a short run view toward price setting, utilis­
ing the principles of ac*ir to the fullest extent and
thereby greatly enhance his short run profits.
However,
It appears that monopolists prefer to take a long run
view, trying to arrive at a price which they think approx­
imates the price which In the long run must just cover
total cost and provide a ”modest” margin of profits.
Hence total unit cost, which only has meaning In the
66
long run, Is relied upon where competition is lacking as a
guide to the "proper** price.
He contends that if he can
determine this long run price which will cover costs plus
a reasonable profit and no more, he will effectively dis­
courage the entrance of competition.
In other words the
monopolist Is concerned about price being too high and
looks to total long run cost as a preventive of this.
On the other hand wherever keen competition exists,
the firms never need worry about setting price too high
for fear of Inviting competition.
The competition exists,
and from the standpoint of price and production planning
the problem Is a short run problem.
As stated In Chapter
2, In the short run, average total unit cost has little
meaning for policy decisions.
The effective guide Is
differential cost*
In view of this background, why Is It then that
economists have the Impression that businessmen, In general,
do not think In terms of differential cost?
business, In general, is monopolistic?
Is it because
We have concluded
that the monopolist tends to Ignore differential cost and
place emphasis upon average total unit costs.
Are most
business concerns monopolistic, thus explaining the econo­
mists Impression that businessmen think In terms of total
cost?
The facts do not support this contention.
It Is
true that there are some Instances In which varying degrees
67
of* monopoly do exist.
However, In the great majority of
companies, competition
is real and makes Itself felt.
This was apparent not only in the companies Included In
the present sttudy, but was also observed In a variety of
companies with which the author came in contact during
v
several years in public accounting practice.
Obviously there is no clear-cut line of distinction
between what is referred to here as monopoly and competi­
tion.
Actually, most business concerns would probably be
classified technically in that type of market which econ­
omists refer to as "monopolistic competition.”
However,
within this overall group there are widely varying degrees
to which competition is felt, and there are many more firms
which tend toward high degrees of competition than toward
high degrees of monopoly.
Consequently there are more
firms interested in the differential cost approach than
firms which are not.
This was definitely borne out in the
firms included in this study.
There was the case cited above of the production ex­
ecutive of one firm who not only thought in terms of differ­
ential cost, but who was so insistent upon this type of
information that he even embarked upon a study of the
technique himself.
This executive cited numerous examples
of instances arising every day in which he applied the mar­
ginal approach.
68
Another executive In a firm manufacturing heavy industrlal equipment, made the statement that he "doesn't
see hov any company can ever make any decision without a
knowledge of differential costs*"
Other examples of this attitude might be cited.
What,
then, explains the economists' opinion that business execu­
tives do not think in terms of margins?
If this attitude
Is not the outgrowth of a general prevalence of monopolistic
conditions, then what can be the cause?
There are a number of factors which would seem to
explain this attitude*
First, of course, there are that
minority of Instances In which the operations tend more
toward monopoly and where It has been demonstrated
executives do become total cost minded*
Economists have
been greatly interested In the Incidence of monopoly In
our economy and have studied it Intently.
If the theory
advanced In this chapter Is valid, then It Is true that
economists have observed the use of average total unit
costs in their studies of monopoly.
A second factor which has contributed to the econo­
mists' attitude Is found In a condition which Ur. Greer
has stressed*
Even where conditions of keen competition
exist, business executives In discussions between themselves
will decry the marginal approach.
trade association meetings,
1 Greer, Howard C., In
Accounting AffEfS&a
prlng Quarter,1950,
In luncheon meetings,
tra<3e publications, etc.,
lectures presented In Accounts £ fiBS!fig&S fPilSJ PctermlnaOhio State University*
69
differential costs are frequently scorned, while the attri­
butes of total costing are acclaimed as a basis for price
determination.
The latter, they say, will provide a fair
price and yet permit each member of the Industry to cover
his cost and allow a reasonable profit.
According to Mr.
Greer, all of this talk is Intended for "the other fellow"5
and the moment an Individual executive is In the privacy
of his own firm, his thoughts turn to marginal thinking.
Mr. Greer says, "As a matter of fact, there seems
to be a conspiracy between accountants and managers not
to talk openly about this subject.
An appreciation that
costs may be lowered by Increasing volume Is thought> to
lead to that horrible abomination, *price-cut ting. *
Cost
accountants dare not mention the devil for fear he may
appear.
I hope there will be less time devoted to
public speeches urging manufacturers to figure In all their
costs to be sure their prices are high enough,and that there
will be more honest studies of the actual savings which
may be obtained through increased volume."’1’
If these observations are valid, then this would be a
further explanation of the Impression which economists
have received.
In other words, business executives have
helped to convey the Impression to economists that average
total unit costs are the guide to executive action, while
1 Greer, op. clt.« gogt RftSflUirgpeRtg, P. 120.
70
there seems to be evidence and support that this is not
true, if their acts are to serve as criteria.
Another important factor which lends much to the
economists' conclusion that executives do not think in
terms of margins is the fact that until recent years most
cost accountants Ignored this approach to costing.
In
other words, the facts would seem to support the contention
that top management in a competitive market has turned to
the differential approach in spite of, rather than because
of, information supplied by cost accountants.
It may be
that the economists'charge of refusal to think in terms of
margins should be directed to cost accountants rather than
to top executives.
There is much evidence that top execu­
tives do think In terms of margins, but one need not go far
into cost accounting literature to gain an appreciation
of the predominance of the total cost viewpoint.
Cost accounting thinking and literature has been
directed toward the long run point of view— that which is
characteristic of financial accounting— and cost account­
ants have resisted change.
It is quite understandable
that economists turning to cost accounting literature in
an effort to discover the businessman§s approach to
costing, would conclude that business uses the total unit
cost approach.
Cost accountants in past years have overlooked an
71
opportunity Tor rendering a real service to management In
the development and use of the marginal approach.
All too
often the cost accountant became so bound up with clerical
details and administrative procedures that his vision of
important fundamentals and basic relationships was cut
off altogether.
When his cost calculations and reports
seemed foreign to management, he was prone to talk about
the education of top management to an understanding of the
work of the cost accountant.
It is now time for the cost
accountant to raise his sights, to cut himself free from
the details of costing and look about him to learn what
the economist, the top executive and others are thinking.
Chapter 4
A Critique of Present Methods of Factory
Overhead Accounting and Control
The title of this chapter Halts the discussion to
the accounting for and control of factory overhead, with
no mention of direct materials and direct labor.
Present
methods of accounting for material and labor are well
adapted to the differential cost approach.
Practically
all of the problems arising In a discussion of differ­
ential costs versus total costs are in the area of account­
ing for overhead*
Accounting for material and labor may Involve exten­
sive clerical procedures, but they are relatively simple
to understand.
Accounting for them is not complex because
the occurrences of these costs is straightforward and
simple.
If a unit of product is produced, the cost is
Incurred; if no production takes place, there is no cost*
There are, of course, some complicating exceptions.
Scrap
and spoiled material develop, and there is idle labor time;
but even these problems have been treated and classified
traditionally as a part of factory overhead rather than
#
problems of accounting for material and labor*
Material and labor cost control have also been rela­
tively simple*
Because these costs behave fundamentally
in a direct relation to units of production, their control,
73
based upon production, has not been complex.
By comparison, the accounting for and control of
factory overhead costs is much more complicated.
This is
true because factory overhead consists of many different
kinds of costs which behave differently in relation to the
production of units of product.
Certain factory overhead
costs are exactly like material and direct labor in that
they vary directly with production.
Other factory overhead
costs remain the same in total amount regardless of the
level of output.
Still other factory overhead costs
Increase in a step-like fashion as production Increases.
The initial classification of costs which is usually
made, however, falls to take into account these fundamental
differences in factory overhead costs.
Practically all
elementary accounting textbooks, or cost accounting texts,
classify factory costs of production as (1) direct material,
(2) direct labor, (3) factory overhead or manufacturing
expenses.
In the short run at least, there is some ques­
tion about the value of a classification of this sort
from the standpoint of cost behavior.
To classify is
"to arrange in a class or classes,"^nd a class 1 5 % number
of objeets, facts or events having common essential properties."
2
In accordance with these definitions, the above
J Funk & Wagnalls Company, College Standard Diction­
ary. *ew Yorkj 194-6, p. 227*
2 Ibid., p. 227*
74
would hardly qualify as a classification.
It Is merely
a listing of costss (1) material, (2) labor, (3) all other
costs.
The first tiro are hardly classes since they consist
essentially of one cost, not a number.
The third Is not
a class since, although It Includes a number of costs,
they do not have "common essential propertied regarding
the behavior of costs.
It is this fact which has caused
the complexities In present methods of accounting for
factory overhead.
It Is true that some overhead accounting techniques
have recognized the existence of different kinds of costs
In the factory overhead category.
The flexible budget and
the break-even chart are two examples of techniques which
do recognize the distinction between fixed,semi-variable
and variable factory overhead costs.
However, many of the
present methods of accounting for overhead Ignore this
fundamental distinction; In fact, the routine methods of
setting standards, accounting and reporting of overhead
make little distinction between fixed and variable elements.
It is these routine methods of accounting for factory over­
head which will be examined here.
Essentially there are two approaches to the account­
ing for factory overheads one Is the purely historical
approach; the other is concerned with the budgeting of
overhead costs through the use of standard overhead rates
75
or predetermined burden rates.
In either approach, the final result is to reduce
total factory overhead to an amount per unit of output.
Where production Is not complex— where only one kind of
product Is being produced— output may be measured In terms
of units of product.
Where, on the other hand, many products
are being manufactured, output Is usually measured In terms
of some factor common to all units of product.
Very fre­
quently the common factor used Is direct labor hours, so
that In either budgeting or In the historical accounting
for factory overhead the net result Is to reduce total
factory overhead to a rate per direct labor hour 14
In the historical accounting for actual factory over­
head, this rate per hour is calculated by dividing total
actual factory overhead cost for the period by the actual
direct labor hours for the period.
Thus, If the actual
total factory overhead in a period amounts to $2,000 and
the firm operated a total of 4,000 direct labor hours, the
factory overhead rate per hour would be 50# ($2,000* 4,000
hours).
There are essentially twe criticisms which are raised
with respect to this procedure.
The first objects to the
treatment of fixed and variable costs as one entity when,
as a matter of fact, they are fundamentally different In
nature.
This Is discussed by Lawrence <Sc Humphreys:
76
"The costs and expenses of a business resolve themselves
into two constants;—
(1) The Direct or Marginal Cost per article— assumed
now to be <£2— which can be designated M.
(2) The sum total of the Establishment or Fixed
Charges of a period...which may be designated F.
"These two constants are independent of each other,
no fixed relationship existing between them.
"In an endeavor to introduce them Into an equation
in order to arrive at something that is often called *total*
cost or 'all in' cost, or by some such term, many people
have been led astray.
"But there is another element that is, for shorter or
longer periods, a fixed quantity— the selling price of the
article; subject no doubt to varying discounts, but the
basic price is, during its durrency, a fixed quantity, S.
"Now, S and M are of the same dimensions— pounds
sterling per article— and therefore subject to the elementary
laws of mathematics.
They can be subtracted to give a
deficit or surplus, or divided into one another to give a
ratio.
On the other hand, M and F, or S and F, are not so
related, and that is the bugbear of the Accountant.
"Why should it be?
"It certainly need not be, if the clear distinction
is kept between the different natures of M and F.
M is a constant ratio;
F Is a constant quantity;
and one® that simple fundamental fact is thoroughly grasped,
all that follows will be clear, and, so far as Costing
and Cost Accounting are concerned, the many pitfalls and
complications encountered can be altogether avoided.
There is a second criticism which is raised in con­
nection with calculating a rate of factory overhead per unit
of output.
The illustration referred to earlier calculated
a factory overhead rate of 50£ per direct labor hour.
From a strictly historical viewpoint, this may not be
objectionable;it may be correct to observe that
past, totalfactory overhead did average 50£
hour which was worked.
in the
for each
The objection arises in the impli­
cation that this 50* is a variable cost and that for each
direct labor hour that the plant operates, a cost of 50*
will result.
This implication may or may not arise in a
historical calculation of an overhead rate, but it is
certainly present when overhead rates are calculated for
budgets and standard*}; and it is in this connection that
the greatest criticism arises*
In order to calculate a standard or budgeted over­
head rate, some assumption must first be made with respect
to the units of output (either products or direct labor
1 Lawrence, F.C., Humphrey*, E.N., Marginal Costing*
Londons MacDonald & Evans, 194-7* PP* 2 and 3*
hours).
This Is necessary In order to know the denominator
of the equation— -the amount by which total factory over­
head cost will be divided in order to arrive at a rate.
It
is also necessary to know the level of output so as to per­
mit the budgeting of the total factory overhead itself.
Since the total is different at each level of output, some
particular level must be assumed in order to make the cal­
culation.
The level of output which is most commonly assumed is
that of "normal" or "standard" capacity.
Thus, if normal
capacity for the plant is 4,000 direct labor hours and the
standard cost of total factory overhead for the output level
is $2,000, then by division, the standard rate of factory
overhead is 500 per direct labor hour.
This is now used as
a budgeted figure, with the implication that for each hour
that the plant will operate, a factory overhead cost of
500 will be incurred.
This technique has made a variable
cost of total factory overhead which, as a matter of fact,
consists of both variable and fixed elements.
To the
extent that there is variable cost in the 500, the figure
has validity and usefulness; but to the extent that the
500 contains a fixed element, it may be misleading.
Dr. Raymond P. Marpie, Assistant Secretary of the
National Association of Cost Accountants emphasized the
seriousness of this when he said*
"It is possible, even
79
probable In my thinking that when the history or costing
theory is written some years in the future, the concept of
normal capacity and normal burden rates will be pointed to
as the Influences which have been most responsible for
retarding the development of cost accounting.
By using
normal burden rates, fixed costs are converted into variable
1
costs.**
Other writers In recent years have joined in the cri­
ticism of normal burden rates and have pointed to some
of the more specific objections in connection with their
use.
One of the primary objections is found in the volume
variances which arise as a result of treating total over­
head as a variable cost.
In the preceding illustration,
the standard overhead rate was based upon a normal operating
volume of 4-,000 direct labor hours and an overhead rate of
50* per hour.
If, In the ensuing period, a volume of other
than 4,000 hours is maintained, a volume variance results.
This is calculated as simply 50* multiplied by the number
of hours of variance from normal.
If 3,600 hours are
actually worked, there is an unfavorable volume or idle
capacity variance of 400 hours (4,000 normal hours minus
3,600 hours actual), amounting to $200 (400 hours x 50*).
If greater than 4,000 hours are worked, a variance is cal­
culated in the same way, but it becomes a favorable or
1 From a letter by Dr. Raymond P. Marple, addressed to
the author and dated July 23, 1951* reproduced in Appendix
B.
80
credit variance.
This volume variance Is now carried to
the Income statement In the period concerned with the effect
that If production varies to any considerable extent, net
Income may be seriously distorted.
Jonathan N, Harris, C.P.A., writing in the January,
1936 Issue of the Bulletin of The National Association of
Cost f c e o ^ t a ^ T was one of the first to criticize this
procedure seriously.
Since that time, a number of others
have added their dissent to the observations of Ur. Harris.
One of these is Hr. I. Wayne Keller, Assistant Controller
of The Armstrong Cork Company of Lancaster, Pennsylvania.
In an address before the Midwest Cost Conference of the
National Association of Cost Accountants meeting In Indian­
apolis, Mr. Keller presented the Illustration shown In
Pigure A on the following page.
This example Illustrates the way In which changes In
production, accompanied by the use of a standard total
overhead rate, may completely alter the net profit picture.
The sales were the same In the first two quarters of the
year, and It may be assumed that costs and expenses re­
mained the same.
Yet, the net profit In the second period
Is reduced by $10,000, solely the result of decreased
production of 20,000 units.
With a factory overhead rate
of 50£ per unit, the 20,000 unit variance equals $10,000
unfavorable volume variance,
in the third quarter, sales'
Basic data*
Standard costs (per unit)
Material and labor
Factory overhead
Total
Sales price (per unit)
(Note: Factory overhead based upon normal
capacity of 1,200,000 units and
$600,000 of cost. Assume no ex­
pected seasonal variance in pro­
duction and sales.)
1.00
_4Q
liS
$ 2.00
. First
-Wwrfor
Units produced
Units sold
300,000
300,000
Sales
Standard cost of sales
Standard gross profit
Less; idle capacity variance*
Actual gross profit
Selling and administrative expenses
Net profit
Second
Third
Quarter
Quarter
280,000
300,000
280,000
300,000
Fourth
...Quarter
350,000
270,000
)(«ar
1,230,000
1. 150.000
$600,000 $600,000 $560,000 $540,000 $2 ,300,000
/ g o ’.ooo /g o .o o o 420.000 4QpQ£ 1.725.000
$150 000 $150,000 $140,000 4135,000 $ 5 7 5 ooo
- 0(25.000)
- 010.000
(15.000)
$i5o,ooo $140,000 $140,000
,000
90,000
90.000
90.000
360.000
■- 9P.000
4 60.000 $ 50.000 S 50.000 i to Iqoo 4 230.000
r
♦assume no price or efficiency variances.
Figure 4. Comparative Income Statement with Varying Units of Production
(Adapted from an unpublished paper presented by I. Wayne
Keller, Assistant Controller of Armstrong Cork Company,
before the Midwest Cost Conference of The National
Association of Cost Accountants, Indianapolis,
Indian, April 4, 1952).
00
H
82
decline as compared with the second period but net profits
remain the same, the result of the fact that production
was back to normal, and therefore no volume variance
occurs. In the fourth quarter, when sales reach an all-time
low, net profit stands at an all-time high due to the fact
that production Is high.
Since 50,000 units In excess of
normal are produced, a credit variance exists of $25,000
(50,000 units x 50£ per unit).
Such unnatural fluctuations In profits are difficult
for management to understand and difficult to explain to
the board of directors.
Management, and most people for
that matter, think of net profits first in relation to
sales.
If costs and expenses remain the same, net profits
should represent changing sales.
The effect of this procedure Is well Illustrated by
one writer as followss
**Due to the relatively high over­
head rate, the comparability of profits to sales volumes
in different periods was heavily Influenced by the level of
factory activity.
In a postwar period, when materials
had become available, the factory was engaged In a program
to rebuild the supply of parts and to manufacture new parts
for new product lines.
The large amount of overhead ab­
sorbed in the Inventory increase resulted In unusual profits.
The comparison of sales volume and profits of this period
to later periods did not make sense to operating management.
83
Had the Inventory decreased substantially in succeeding
periods, comparisons would have been even more dispropor­
tionate, since cost of sales in this later period would
have Included fixed expenses of the previous period carried
forward as inventory, in addition to fixed expenses of the
later period of lower volume, charged off as unabsorbed
1
overhead,"
Another writer prepares an illustration essentially
like that presented in Figure 4, and says:
"Here is a
case where there were identical sales figures for the two
succeeding months, yet the operating profit shown is three
times as large in one month, as in the other.
The differ­
ence is of course accounted for by the fact that production
was at a high rate in January, so that factory burden was
over-absorbed and the lower production rate in February
resulted in an under-absorbed burden.
what is the correct profit?
The question arises,
Should we say that the rate
of factory production In a month should be allowed to
influence profit regardless of the rate of sales in the same
month?"
2
The existence of this volume or idle capacity variance
1 Chambers, Charles R. , "A Conversion to Direct Costs",
Ballgtl^of TheHatlonal Association of Cost Accountants.
2 Nalklrk, W.W. , "How Direct Costing Can Work for
Management", Bulletin of Tfc* Hk.tlffiaKl
s £ £fi2£
Accountancy. January, 195!» p. 524.
84
is purely the result of the attempt to make fixed over­
head variable.
The overhead rate (50£ in the above exam­
ples) Is applied to units of production as though it were
variable.
Then, since it is not entirely variable, when
volume does not equal what is considered normal, some
disposition must be made of the under-applied or overapplied variance.
If overhead were entirely variable,
the procedure would be logical and justified.
Some other questions may be raised regarding the
meaningfulness of the variances resulting from the use of
normal or standard overhead rates.
Usually three overhead
variances are developed which are Intended to explain
deviations from standard overhead.
One of these variances
we have already examined— the Volume or idle capacity
variance.
The other two are the production efficiency
variance and the budget variance.
These three variances are developed and Illustrated
in nearly every cost accounting textbook and have been used
in various N.A.C.A. publications.
Terminology, however,
may vary.
The terminology used here is taken from
1
Blocker's Cost Accounting.
The National Association of
Cost Accountants in a Research Series Monograph on standard
costs says:
"There are three factors which can cause
overhead variances— namely, production volume, production
1 Blocker, Jbhu. G., Cost Accounting. New York; McGrawHill, 19*8, p. 391 ff.
time, and spending.1
*1 These are exactly the same as the
idle
capacity variance, the production efficiency variance
and the budget variance.
An example of the way in which these variances are
calculated will be helpful in their discussion.
Assume
the following basic data:
1.
Standard overhead for the budget period
2.
Standard units of production for the
budget period
3*
4.
Standard labor hours for the budget
period
$2,000
400 units
4,000 hours
Standard labor hours required for
production of oneunit (3f2)
10 hours
With these assumed conditions,the standard rate per
direct labor hour Is determined by the methods discussed
earlier:
,. = 504 per direct labor hour
4,000 hours
and now, since it requires ten hours to produce a unit of
product at 50£ per hour, there would be standard factory
overhead of $5*00 in each unit produced.
At least this
would be true if all factory overhead were variable.
Continuing, assume the following conditions with
respect to actual operations during the budget periods
1 National Association of Cost Accountants, Research
Series Monograph, How Standard Costs Are Being Used Cur­
rently. 1948, p. 60.
5.
Actual overhead for the period
6.
Actual units produced during the period
7.
Actual labor hours Tor the period
At
$1,990
350
3800
the end of the period, the total overhead var­
iance would be calculated as follows*
Actual factory overhead
$1,990
Standard overhead (350 units (® $5)
1,750
Total overhead variance
$
240
The total overhead variance of $240 may now be divided
into Its three causes as follows*
1.
Idle capacity variance (which has already been
discussed)*
Budgeted hours of plant operation
for theperiod * 4,000 hrs.
Actual hours of plant oper­
ation for the period
- 3r8QO hrs.
Unused hours
Cost of unused hours,
200 @ 5* $
2-
200 hrs.
=
$100.00
asSiPtt tftiglfflCT, iwrlftflcg*
Actual hours required to produce
350 units
- 3>800 hrs.
Standard hours required to
produce 350 units
(350 x 10 hrs.)
Excessive hours required
for production
Cost of operating the plant
300 excessive hrs.
(300 x 50*
=
= 3,500 hrs.
hrs.
$150.00
87
3.
Budget variances
Budgeted overhead for the period $2,000
Actual overhead for the period
Saving In reduced overhead
Total variance per above
l r99Q
C 10.00)
$24-0.00
The Idle capacity variance, as we have already seen,
would be more valid If all factory overhead were variable;
and the objection which Is raised results from the existence
of a fixed element In overhead.
Essentially this same
criticism may be levied against the production efficiency
variance.
This variance would lead management to chastise
the labor force for having operated the plant too many
hours for what it produced.
But clearly this cost Is only
the variable cost of the excess hours of work— the portion
of the 50£ per hour which Is variable.
The other portion—
the fixed— Is a cost anyway and has no relation to exces­
sive hours of operation.
This whole subject will be devel­
oped In greater detail in Chapter 5, but a little Illustra­
tion may be given.
Assume for example that of the $2,000
budgeted overhead for the period, $1,000 is fixed for any
level of output and that the variable element amounts to
25* per direct labor hour.
If this were the case, the .cost
of the 300 excessive hours would be $75 (300 hours x 25#).
In other words the overhead cost of production Inefficien­
cies Is only the variable cost, while the rate Includes
88
both fixed and variable.
While the Idle capacity and the production efficiency
variances seem to be based upon the false assumption that
all overhead costs are variable, In contrast the budget
variance seems to Imply that the overhead Is entirely
fixed.
When production was budgeted at 4-00 units and
4,000 hours, overhead was budgeted at $2,000.
The calcu­
lation of the budget variance does not take Into consider­
ation the fact that the operations were far below this
anticipated level— production units down to 350 from
anticipated 400, and hours down to 3,800 from anticipated
4,000.
Since a portion of overhead Is variable, decreased
productive activity means some decrease In cost; but this
Is not recognized In the budget variance computation.
With such a decline In volume, It might be assumed that the
total overhead cost should have properly declined much
below $1,990 and accordingly, this might represent a very
nnfwiroraM m variance.
But the actual calculation takes
none of these factors Into account, treats overhead costs
as purely fixed and reports a $10 favorable variance regard­
less of what has happened to volime.
All of these questions regarding the traditional
treatment of normal overhead rates lead one plant controller
to observes "we have completely dispensed with the use of
the traditional overhead variance accounts.M
There Is still another phase of present methods of
overhead accounting which gives rise to some questions of
logic.
Reference Is made to the arbitrary allocations of
fixed cost which must be made In order to arrive at the
portion applicable to each unit.
There are many costs
which have only a very Indirect relationship to units of
specific produet; and these costs are arbitrarily allocated,
then arbitrarily re-allocated and then re-allocated again
before they are finally reduced to a per-unit basis.
Examples of such costs are personnel manager's salary,
past service eost of pension plans, the plant Infirmary,
the eost of a house organ or supporting a company baseball
team.
Not only do all these costs remain the same within
wide ranges of productive activity, but they are only re­
motely Identified with widely varying types of products.
Host common procedure Is to allocate these eosts first to
departments— productive as well as service— on some se­
lected basis.
Service department costs are then reallocated
to productive departments on some selected basis.
Finally,
overhead costs of productive departments are allocated to
units of product, again on some arbitrary basis such as
machine hours, labor hours, labor cost, etc.
One writer cites an example of the laek of correla­
tion betoreen these arbitrary eost calculations and any­
thing relating to product value.
He sayss "I am reminded
of such a situation which occurred only recently.
Two
competing manufacturers of women's apparel turned out a
skirt which was nearly Identical because of similarity
In design and because both used the same fabric with a
highly stylized print.
Manufacturer A's selling price was
$4.75 while Manufacturer B's price was $3.75*
Naturally,
A's selling price became $3.75 promptly, despite the fact
that, according to his cost sheet, he was making no profit
at this price.
It then happened that one of B's cost
sheets became available to A.
The management was amazed
to see that B appeared to have a comfortable margin at
$3.75.
"How was this possible?
The companies had very
similar establishments In the same district and their
annual gross sales were nearly the same.
Comparison of
the cost sheets revealed that the difference In direct
labor and material was negligible but that drastically
different rates were being used for Indirect cost al­
location.
It was this which made It appear that virtually
the same skirt was being produced at two different
costs
Most of the techniques discussed In this chapter are
a result of an effort on the part of eost accountants to
Indlr
Cost
1 Sapega, Andrew S., "More Useful Accounting for
jog of
, sepxemoer, xypi, pp. 23-2+.
calculate average total costs per unit, Including in each
unit a proportionate part of the firm's fixed cost.
This
total cost seems Important so that it may he compared with
unit selling price, and a net profit per unit may be cal­
culated.
But of this net profit per unit, Lawrence &
Humphreys says "no one unit ever makes a profit.
Net profit
is made only from total activity of manufacturing and
distribution during £ period, and the units made and
sold contribute their quota to a pool from which the profit
finally emerges."1
It may appear logical to make these total cost alloca­
tions to product; but if these techniques are not conveying
information to management in a clear and understandable
manner, they are not achieving their full usefulness.
1 Lawrence A Humphreys, pp,,cl$. , |frrjEjpft?. Costing.
P. 4*
Chapter 5
Adapting Accounting Techniques to the
Differential Cost Approach
Thus far the discussion has dealt primarily with the
theoretical background for differential costs and ob­
jections to present costing procedures.
It is the ob­
jective of this chapter to develop specific ways and
means of Incorporating differential costs In the accounts
budgets, reports and other accouhtlng techniques.
As with all cost accounting, the problem resolves
Itself Into two phases.
One of these Is concerned with
the use of cost data for special cost studies; the other
has to do with the routine accounting and reporting of
costs in regularly established procedures.
Cost account­
ants have always worked In both of these areas.
The
Introduction of differential costs does not alter this
setting but merely provides the cost accountant with a
new tool with which to approach these problems.
Differential costs were first applied to the solu­
tion of special cost problems and have had more attention
In this application.
Textbook treatment of differential
costs Is almost solely in this area.
Only in very recent
years has there been any discussion of the application of
differential cost techniques to routine accounting and
reporting, and there Is comparatively little written on
93
this phase of the problem.
Since there has been more ex­
perience with the application of differential costs to
special cost studies, this area will be examined first*
By special cost studies are meant the preparation of
cost estimates or other cost data for spedlfic proposals
or problems confronting the firm.
This was discussed in
Chapter 1 when the advantages of the differential approach
in this situation were outlined.
Examples were cited and
several detailed illustrations given.
It will be recalled
that, broadly speaking, there were two types of situations
involving estimates of differential cost and differential
revenue.
First, there are proposals directly concerned
with changes in unit output of production, accompanied by
changes in revenue.
Examples of this are found in opening
or discontinuing a new territory, adding or discontinuing
a product line, acceptance of a defense contract, etc.
Secondly, there are special cost studies initiated with
respect to proposals which may Involve only a revenue change
or only a volume change or neither one.
Examples of this
would Include projected plans for the adoption of a product
guarantee, the manufacture of a part hitherto purchased,
the design and construction of a machine in our own shop
as opposed to outside purchase, or the provision of some
service or benefit for employees.
The distinction between
these two broad classes of special cost problems is
94
Important because the major attention has been applied to
the differential costs of changes In units of output and
revenue.
One application of the differential cost tefahnlque
has been in the so-called "break-even” chart.
This Is a
means of presenting graphically the relationship of costs
and profits to changes In volume.
The device has been In
use for many years, one of the earliest proponents being
C. E. Knoeppel, an early Industrial management counselor
and disciple of Frederick W. Taylor and Henry L. Gantt.
Knoeppel claims to have originated the Idea of the break­
even chart In the year 1909, although he called it the
-i
Knoeppel "Profltgraph".
-L
Since that time there has been
little change in the basic concept of the break-even
chart, but It has grown In popularity.
In Its Amplest form, the break-even chart consists
of tiro plotted lines, as In Figure 5 on the following
page.
One line— B, D, C— represents total cost of pro­
duction, selling and administration at each volume level;
the other line— 0, D, A— represents total revenue at each
level of output.
The revenue line— 0, D, A— starts at
zero since there Is no revenue when there are no sales.
The total cost line, on the other hand, starts at a point
1 Knoeppel, C.E. , Profit Engineering. New Yorks
McGraw-Hill, 1933, p. IX.
Dollars (Thousands)
7-
Unlts (Thousa nds)
Figure 5*
Simple break-even chart.
9$
of no production but of those fixed or sunk or shut-down
costs incurred even when there is no production.
illustration this point is at $2,000.
In this
D is the volume at
which the revenue exactly equals cost--the break-even point.
At all volume levels greater than D the revenue line ex­
ceeds the cost line, the difference representing profit.
At all volume levels less than D, cost exceeds revenue
and loss results.
Further refinements in the hreak-even chart have been
concerned primarily with greater detailed description of
what makes up total cost at the varying levels of output
(Figure 6).
The break-even chart has been a valuable adjunct to
accounting for differential costs.
Although it has served
other purposes, one of the most beneficial has probably
been the fact that it has greatly advanced an understanding
of the differential eost principle.
The chart has gained
widespread popularity and has therefore conveyed to many
cost accountants some notion of the relationship of costs
and profits to volume.
In addition, the chart can be useful In gaining a
broad estimate of the effect of broad changes in volume
and may be of considerable value as a guide in gaining an
overall perspective of the operations of the firm.
However,beyond these broad generalizations, the use-
97
Profit after taxes
/ Income taxes
8
7
Selling
Pro:
Dollars (Thousands)
6
Administrative
Variable
" Expense
4
3
Manufacturing
2
Selling
Fixed
Expense
1
Administrative
Manufac turing
0
Units (Thousands)
Figure 6.
Detailed break-even chart
9$
fulness of the chart becomes somewhat limited.
William
L. Fill says:
“The break-even chart is just a summary
report. Its simplicity enhances its ability to com­
municate the relation of sales less variable and
fixed costs at different levels of operation
quite forcefully to financial analysts outside
the company and to the management group within
the company. In such a function, its use to
convey the information In the master budget Is
undisputed. However, the preparation of a
break-even chart requires many estimates and
conjectures which may add up to minor inaccur­
acies in the chart which will be misleading if
the chart Is used to measure costs and sales at
any particular level of output. Especially is the
break-even chart unreliable when output ap­
proaches the break-even polnt--almost invariably
the break-even point will begin to shift as it
Is neared. The chart, then, has uses as a
summary report and portrays the general facts
of the company as the landscape would be in an
oil painting. To abuse the report by using It
as a detailed aerial photograph to direct actual
movements of the management forces Is to court
disaster.w
Although the break-even chart serves a very useful
purpose, It would be of little help In the preparation
of detailed cost studies for most concerns.
Its primary
disadvantage is over-slmpllflcatlon and lack of realism
for detailed purposes.
In the first place, plant activity is stated entirely
in terms of units of product, and then only one kind of
unit of product.
This would be of significance In a
plant which manufactured only one kind and one size of
unit of product.
One such plant was visited In this
i' .s
1 Fill, William L., “The Break-Even Chart,n The
Accounting Review. April, 1952, p. 203.
99
study.
This firm manufactured one product only, consisting
of three simple parts, two of which it manufactured, the
third of which it purchased.
In such circumstances,
changes in volume usually follow simple progressions and
can be plotted simply.
However, for plants manufacturing
a complex group of products, it is Impossible to plot
units of product in a meaningful progression.
In an effort to correct this difficulty for plants
which manufacture several products or a "mix" of products,
the horizontal axis, or the volume scale, might be stated
in terms of a volume factor which is common to all units
produced.
Such a common factor might be direct labor
hours or total plant machine hours, etc.
These may be
stated in terms of hours or may be converted into terms of
plant capacity stated as a percentage.
Thus, the chart
would reflect total eost and revenue at each level of
total plant hours within the meaning of this term.
Bven this approach, however, would not be entirely
satisfactory, particularly where products differ widely
in costs and methods of production and where the operations
performed in various departments differ widely.
Under
such Circumstances, in order to arrive at total eost at a
particular level of plant operating hours, it would be nec­
essary to assume a certain "mix" of products.
With
100,000 man hours, an unlimited number of combinations
100
of different products could be manufactured, each with a
different cost and revenue total.
Therefore, the con­
struction of the break-even chart would be dependent upon
the particular mix of products which Is assumed, and It
would be useful only as long as that particular mix was
maintained.
The chart, under these circumstances, would
have little usefulness for most special cost studies.
For example, In one of the firms studlesC, a proposal
was under consideration which Involved the manufacture of
a new product In only one of the plant1s many departments.
This particular department had some idle capacity, so the
plan was to manufacture a simple product which required
ohly the facilities of this one department.
This action
would, of course, completely alter the existing pattern of
product "mix” in a break-even chart prepared for this
company.
In essence the break-even chart would have usefulness
in special cost studies only where It was proposed to
make shifts In volume which exactly corresponded to volume
fluctuations assumed when first preparing the chart.
It
would have little usefulness where volume consists of a
"mix" of products, or in the case of special proposals
which are not concerned with changes In volume.
Other serious shortcomings of the break-even chart
are mentioned by V. L. Fill, "Other assumptions Involved
101
in computing the sales to be plotted at various levels of
production are that prices are fixed, that there Is but
one product or that the sales 'mix' does not change and
that If prices do change the percent of sales in excess
of variable costs remains constant.
These assumptions
should be given serious consideration In the preparation
and review of a break-even chart and if not true, a new
chart may have to be prepared."1
Since we have concluded that the break-even chart
is useful only for very broad approximations, It might
seem pointless to argue about refinements with respect to
the behavior of either the revenue or cost curve.
Never­
theless, to enable the preparation of accurate cost studies,
it is Important to have as full an understanding as possible
of the specific behavior of these elements.
For this
reason, closer scrutiny of the cost and revenue lines are
in order.
The question being raised with respect to the behavior
of revenue pertains to the distinction between the various
types of markets which was discussed In Chapter 2.
2
The
revenue lines depicted In Figures 5 and 6 are typical of
most break-even charts— namely, they are perfectly straight
lines.
This Implies that revenue varies exactly
1 Ibid. Fill,"Break-Even Chart", p. 203.
2 ££*_&£££•» PP. 35 ff.
102
proportionately to output at all volume levels; or In other
words, the product can be sold at the same price per unit
regardless or the number of units sold.
This Is the con­
dition which exists In the type of market which tends toward
the economists' concept of pure competition.
The Individual
firm has no control over selling price and can sell all of
Its output at the established market price.
Although this
pricing condition does exist in many firms, It Is far from
typical In. many types of Industries.
In monopolistic competition the firm has some control
over price, and usually It reaches a point where added
t
volume can be sold only by reducing the price.
In these
circumstances the revenue curve Is not a straight line,
but eventually would tend to become more horizontal as
more and more units are sold.
Another over-simplification In the break-even chart
is found In the assumption that the total cost line is
straight.
There Is first the possibility of periodic
"steps" In total cost resulting from what is commonly
termed semi-variable cost.
However, we shall Ignore this
possibility for the moment, since we shall deal with It
at greater length later.
Even if we Ignore these "steps” ,
It Is still doubtful whether the total cost line would be
perfectly straight.
Economists have always depicted the
total cost curve of a firm as a curved line, resulting
103
from the principle of non-proportional returns.
In other
words as volume Increases, a point is reached where inef­
ficiencies begin to occur;and costs will rise more rapidly
than volume.
If these two lines— total revenue and total cost—
did not curve but rose steadily In exactly the manner
depicted in Figures 5 and 6, it would appear that a firm
could Increase its profits without limit by merely increas­
ing its output.
This is unrealistic.
Figure 7 shows a break-even chart in which the two
main lines— the revenue line and the total cost line— are
drawn to conform with the principles discussed above.
Total revenue— 0,A— does not go on increasing forever at
the same rate but tends to flatten out as output becomes
great.
Total cost— B,C— likewise curves upward as inef­
ficiencies cause total costs to rise more rapidly than
does output.
If carried to an extreme, point Y is even­
tually reached where total cost once again exceeds total
revenue.
M,N— the greatest distance between total cost and
total revenue— represents the level of maximum profit.
The same principles may be observed in the following
data from which Figure 7 was plotteds
104
Total
S.Pg£.
Volume
-O -
$
Differential
2,000
1,000
2,500
2,000
—
Total
Revenue
-
Differential
Revenue
0-
—
500
$2,000
$2,000
3,100
600
3,500
1,500
3,000
3,900
800
4,600
1,100
4.000
5,000
1,100
5,400
800
5.000
6,500
1,500
6,000
600
$
If the total cost and revenue lines were perfectly
straight, then the differential cost would be the same
for each Increment of output and so would the differential
revenue*
On the contrary, In this example, differential
cost is increasing at an increasing rate and differential
revenue is decreasing at a decreasing rate, resulting in
the curved line shown in Figure 7 •
It might be argued that these refinements are too
theoretical and are unnecessary for practical uses.
Devine
sayss **a number of studies designed to test the constant
variable cost assumption have shown that for many concerns
over the range of normal output this assumption is Justi­
fied."1
It is probably true that for the broad approxima­
tions of the break-even chart, perfect variability may be
a simplifying assumption; although it was evidenced in
1 Devine, Carl Thomas, £2fit AgggmfrLflg
New Yorks The Macmillan Company, 1950, p. 583*
ADfiJLXllS*
105
7
Dollars
(Thousands)
6
5
4
3
2
1
O
Units (Thousands)
Figure 7. Break-even chart showing
decreasing total revenue and increas­
ing total cost
10$
several firms that this change In the rate of variability
is a very real factor.
Even If it Is not Important for the
break-even chart, It Is important In detailed cost studies.
Devine says that the variability assumption is valid "over
the range of normal output.H
Experience shows however that
much of the time the firm Is operating at something other
than "normal" output, and many cost studies are undertaken
with respect to sub-normal or above-normal output levels.
This was particularly evidenced In the heavy machinery
firms which were visited.-they described themselves as a
"feast or famine" industry.
little significance for them.
The concept of normal was of
An executive in one firm
estimated that four years ago they were operating at about
60$ of "normal capacity," while today he would estimate
the figure at around 130$ of capacity.
This was not an
Isolated case; similar experiences were reported In other
firms.
Not only did this demonstrate that the concept of
"normal" capacity has limited usefulness, but the same
executive confirmed the declining efficiency and the in­
creasing costs at these upper reaches of output.
In his
words he "picked up a lot of fat" at these upper levels
of output which could be trimmed when output was reduced.
It Is evident that a consideration of the changing
variability of costs and revenues should be considered In
107
a break-even chart, and it is certain that these are impor­
tant in special cost studies*
In an effort to provide more detailed Information
than is available in the break-even chart, the flexible
budget has been developed (see Figure 8).
The flexible
budget shows essentially the same information in detailed
dollar and cents form as does the break-even chart in
graphic form.
Although this form of the flexible budget
has served many useful purposes, when it is prepared in
this summary fashion for the total firm it is subject to
essentially the same limitations as the break-even chart.
It is somewhat more detailed; and by a breakdown of the
semi-fixed expenses, it provides a clearer view of the
"steps** in total costs than does the break-even chart.
Yet this budget for purposes of calculating differential
costs is limited essentially to changes in units of pro­
duction, whether stated In terms of units or man-hours or
machlne-hours•
In cases where a single product is man­
ufactured or where production is not complex, this type of
flexible budget might be sufficient.
In firms producing
a mixture of products, a particular Mmlxn would have to
be assumed in preparing the costs at the various volume
levels of the budget.
In this event the budget is not of
much value in studying costs, except for proposals which
conform to the assumptions underlying the budget itself.
1081
Volume
Fixed costs;
ManulSciuring fixed costs
Selling fixed costs
Administrative fixed costs
Total fixed costs
Semifixed costs;
Manufacturing costs;
Supervisory salaries
Light and heat
Total manufacturing costs
Selling costs;
Salesmen's salaries
Insurance and taxes
Total selling costs
Administrative costs;
Clerical salaries
Insurance and taxes
Total administrative costs
Total semifixed costs
Variable costs:
Manufacturing costs;
Materials
Labor
Repairs
Power
Total manufacturing costs
Selling costs*
Commissions
Travel
Total selling costs
Administrative costs;
Office supplies
Total variable costs
Total costs
Number of units produced
Average cost per unit
60£
n
$200,000
$200,000
$200,000
$200,000
$200,000
$200,000
$200,000
120,000
120,000
80,000
120,000
80,000
$i*oo;ooo
120,000
80,000
120,000
120,000
80,000
$1*06,0o6
120,000
80,000
$1*06,660
80,000
8055
120$
n
.
$1*507005
80,000
$1*00,600
$ 1*2,000
8,000
$ 50;000
$ 1*6,000
9,000
$ 55,650
$
$ 35,000
$ 29,000
6,000
$15,005
1*6,000
9,000
$ 55,000
$ 1*6,000
9,000
$55,060
$
9,000
1,000
$15,(505
$ 9,000
1,000
0 5 ,(5 5 5
$ 11,000*
2,000
$ 13,006
$ 12,000
3,000
$15,665
$ ll*,000
li,000
$ 18,600
$ ll*,000
1*,000
$ 18,600
$ H*,ooo
Looo
^187665
$ li,000
1,000
$ li,000
1,000
$ 5,005
$l* 5,o 6o
$ 5,000
2,000
$ 7,000
3,000
$ 8,000
1*,000
np55
$"85,666
$ 35,000
56,000
3,000
2,000
n o w
$ 60,000
100,000
109,000
120,000
$389,060
O T W
$1*00;055
$ 25,000
$ 25,000
5,000
npjo
5,000
$ li>,556
$ 33,000
51t,ooo
2,000
1,000
$15^05
$ Hi,000
Looo
r m
5,000
$113,555
O T 55
"wm
$ 15,000
5,000
T O 55
$ 17;ooo
$107000
$ 8,000
I*,000
$ 12,606
$ 55,000
fT p o
$13^55
$ 8,000
1*,000
$ 12,666
$85,666
$ 1*0,000
61*,000
7,000
$ 1*5,000
72,000
21,000
12,000
$ 50,000
$ 55,000
80.000
90.000
$i5o!ooo
1*0,000
27.000
$1377655
79.000
58.000
$282,006
$17,000
7,000
$21*;005
$ 19,000
9,000
$ 28,660
$ 22,000
12,000
$31*;666
$ 1*1*,666
8,000
$182,660
$557305
966,oo6
r r a
10,000
13,000
18,000
$2351655
1325,000
$811*,060
1,100,000
$ 0.71*
$l*5i;000
$936,666
1,200,000
T o J
5,000
?m;o6 5 .
$ 16,000
6,000
6,000
7,000
D
$5&£000
■'755,'555
$ ” 531
$lli5;600
$600,000
860,600
Figure 8. Flexible Budget
(Adapted from Blocker, J. G.,
"Cost Accounting," pp. 67U-675.
New lorkj McGraw-Hill, 19U8.)
$726,T O
1,000,000
$ w
$ 27,000
17,000
In plants which have a complex of operations and
products, It becomes necessary to understand the behavior
of costs In each operation*
By operation Is meant the
performance of a function for costing purposes.
Usually
such functions are termed cost centers or costing depart­
ments or just simply departments.
However such a depart­
mental organization for costing purposes does not necessar­
ily conform to departmental organization for administrative
purposes.
The objective here Is to divide the total plant
into centers wherein a single function is being performed.
Detailed budgets can then be prepared for costs of operating
this one function at various volume levels.
Now when a
specific proposal Is made, It will first be analyzed In
terms of functions or departments Involved.
Then turning
to the cost budget for each of these departments, prepared
in terms of activity level, the differential cost of adopt­
ing the proposal can readily and accurately be determined.
It was pointed out that the type of flexible budget
prepared for the plant in total was valid and useful only
if the plant were manufacturing essentially a single
product, or had only * single process.
The proposal here
is to make each department in a complex plant just like a
small firm which manufactures a single product in a simple
operation.
If all of the products passing through a depart­
ment do not have the same operations performed on them,
110
then the cost centers have not been carefully enough defined,
and two or more costing departments may be needed.
Once a careful determination of departments for cost*
ing purposes has been achieved, a careful study of the
operations and costs of each department must be made.
First, a careful listing of each cost or an account
classification should be prepared for each department
showing each variable and semi-variable cost pertaining
to the department.
Fixed costs may be excluded.
Since our objective Is to provide a basis for differ­
ential cost calculations and since fixed costs have no
part in differential cost studies, they will not be in­
cluded in the departmental budget.
A separate budget of
fixed costs should be prepared, and the budgeted figures
compared with actual figures for proper control purposes.
By no means can fixed costs be Ignored; in fact, they con­
stitute an Important area for accounting and managerial
scrutiny.
However by the very definition of differential
costs, the fixed costs are excluded.
The budget of fixed costs might be prepared first on
a plant-wide basis, and for differential cost purposes
this would suffice.
Determination of fixed costs on a
departmental basis is likely to Involve many arbitrary
allocations which may raise some questions as to the
reliability of the results.
This was discussed at the
Ill
close of* Chapter 4.
If total cost Information is desired
for any purpose, fixed costs may be allocated to departments
and then to products*
However such a procedure Is not a
part of a system of differential costs*
One of the firms included In this study was in the
process of developing.this type of budget.
The express
objective of the project was to make possible the prepar­
ation of detailed cost studies of each plant operation
under varying levels of activity*
The plant was first departmentalized on a Ncost
accummulation" basis— that is the plant was broken-down
Into cost activity centers, each constituting a depart­
ment.
A chart of accounts was then prepared In which
the costs of each department were listed and classified as
either variable or semi-variable.
A simple example, adapted
from this company's chart of accounts, Included as variable
expenses In one department!
Account 891 Machine Direct Labor
Cost of machine operators will be charged to
this account for the entire time that they
are available at the machine for the purpose
of operating the machine*
Account 802
Manufacturing Supplies
This account will be charged for the cost
of all operating supplies used in the
112
operation of this department.
Includes
lubricating oils, greases, and other
supplies used In operations.
Account 803
Waste and Spoilage
Charges to this account will originate In
the Accounting Department and will repre­
sent the total cost of spoiled work.
Also
includes any cost Involved In salvaging
defective work.
Account 804
Electric Power
Charge with the consumption of electric
power as reflected by meter readings.
Account 805
Fuel
Charge with the consumption of gas as
reflected by meter readings.
Account 806
Repairs
Labor and materials used in repairing
equipment assigned to this department.
e
Semi-variable expenses are thosAwhich change In a
step-like fashion as productive volume changes.
A seml-
varlable expense will remain the same in total over a
given range of volume; then at a particular point, as
volume Increases, it will "Jump" In amount to a new level.
At this point It again remains the same over a given range
of volume.
Figure 9 reflects a common way of presenting,
113
8
s6 01
c
rf
o
xj
Eha
m
u
tin
33
O
«
T
2
3
4
5
6
Units (Thousands)
Figure 9* Typical behavior of a
semi-variable cost
8
H4>
graphically, the behavior of a semi-variable expense.
Examples of semi-variable expenses adapted from the
Illustration mentioned above, included:
Account 810
Indirect Labor— Foremen and Floorboys
Charge with salaries and wages paid foremen
and floorboysi
Account 811
Indirect Labor--Janitor
Charge with salaries and wages paid for
Sweeping, cleaning and Janitor service.
Account 812
Departmental Mechanics
Includes salaries of all mechanics assigned
to and,carried on this department's payroll.
These are but a few examples of the types of variable
and semi-variable expenses included in a chart of accounts
for one department.
The next step in the preparation of the budget for
this department is the determination of a unit of measure­
ment.
Since we are dealing entirely with variable ex­
penses (either wholly variable or semi-variable) we must
now have a unit to measure the work being performed or
volume of activity in the department.
If the department processes only one kind of product,
then units of output would constitute a perfect measure of
activity.
However where work is being performed on units
of varying size and complexity, the number of units produced
115
would not constitute a satisfactory measure of the level
of output.
In such Instances some other common unit of
measure must be found.
This should not be difficult
since each department is performing essentially a single
type of operation.
Thus a satisfactory unit of measure may
be found In direct labor hours within the department or In
machine hours or direct labor cost.
That unit should be
chosen which most properly measures the level of output of
the department.
The procedure for establishing budgeted amounts for
each cost will now follow the well established routines
for budgeting.
Particularly In the case of the variable
costs, ho new problems would arise.
Budgets here would be
based upon past experience and standardized performance,
adjusted to reasonable emxpectatlons of actual future
performance and stated In terms of a dollar amount per unit
of measure.
Thus budgeted direct labor cost may amount
to $3.15 per machine operating hour, and repairs are budget­
ed at $.10 per machine operating hour, and waste and spoil­
age at $.07 per machine operating hour, etc.
The important factor to be remembered In budgeting
the semi-variable expenses Is that a budgeted figure must
be determined for each "plateau" In the upvrard progression
of the cost (see fflgure 9).
This Involves two principal
tasks— first, determining the volume levels at which the
116
"step" occurs and secondly, determining the amount of the
cost at each "step"*
An* Illustration of hcmr the semi-variable cost budget
may be prepared is shown in Figure 10 on the following
page*
This was adapted from the procedures being developed
by the company which was referred to earlier in this con­
nection*
This company sets up what they call a "Budget Rate
Development Sheet" for each expense in each department.
The most Important part of the sheet is the rate Itself
shown at the bottom of the page.
However the computations
followed in arriving at the rates are given in the upper
part of the sheet so as to formalize the calculations and
form a permanent record of them.
The sheet presented in Figure 10 illustrates the cal­
culation of the cost rate for foremen and floorboys (Ac­
count 810).
It should be noted in this illustration that the
first factor determined was the output levels at which the
semi-variable cost "jumped."
These levels in this case
are first stated in terms of shifts, for it is with the
change in the number of shifts that the cost changes.
These levels are then converted into terms of machine
operating hours (Iffoh), the unit of measurement in this
department.
The basis for this conversion is presented
117
Department_____ In.jection molding____ Account Number_____ 810_____
Account description
Foremen and Floorboys* s a l a r i e s __________
The foremen and floorboys* salaries in this department should be as
follows, by level of activity:
Total Total
Max.
Number Days
Std.
Number
Fore­ Floor­
Semi-fixed
men
cost
1. Shifts /Wk. Machines
men
moh.
1
1-2
0
340
1
$ 309.40
5
1
1
680
567.80
1
5
3-4
2
2
2
1,360
1,152.60
5
3-4
2,040
1,737.40
3
3
3/
5
3-4
4
L
3-4
3
7
2,870
2,316.76
3,588
3
2,316.76
7
4-5
4
4
5-6
4.306
3
4
___
2.575.16
7
2. 1 shift 1 machine 5-day wk.*(3^5-104 Sat. & Sun, - 6 Hoi.) £ 12 Mo.
x 8 hrs.s 170 hrs.
3 shift 1 machine 7-day wk.r(365-6Hol)il2Mo.
hr s.- 717.6 hr s.
3•
1st Foremen Monthly Cost
170 x 1.82
$309.40
2nd & 3rd Foremen Monthly Cost
170 x 1.87
317.90
170 X 1.854
4th Foreman Monthly Cost
315.80
1st & 5th Floormen Monthly Cost
170 X 1.52
258.40
2nd & 3rd Floormen Monthly Cost
170 X 1.57
266.90
_____ 4th Floorman Monthly Cost
265.18
170 X 1.554
Date
Accepted
Approved
Unit of
Semi­ Measure
fixed Activity
budget Level
Budget
rate
Var­
Unit of
iable Measure
budget Budget
rate
Std.
moh.
Up to
340
Std.
moh.
341 to
630
Std.
moh;
680 to
1360
Std.
moh.
1360 to
2040
Std.
Std.
moh•
moh•
2040 to Over
3588
3588
$309.40 $567.80 $1152.60 $1737.40 $2316.76 $2575.16
Figure 10.
moh = machine operating hours
Budget rate development sheet.
118
In Section 2 of the sheet.
After stating each of the changing levels of activity
in terms of the unit of measurement, the cost for each
level is calculated.
Section 3 sets forth the cost of
foremen and floorboys for each shift.
These costs are
then applied to the number of foremen and floormen required
for each activity level to arrive at the cost for each
level.
These cost determinations are then carried to the
summary at the bottom of the page, the final objective
of the budget sheet.
Here then is an exact determlnation
of the eost of this semi-variable expense at each possible
output level.
There Is no need for an unrealistic assump­
tion of a NnormalM operating level which must be made where
fixed costs are.Included•
The only consideration Is of
variable costs which can be determined directly, positively
and reallstlcly at any activity level.
It should be noted
that this same "Budget Bate Development Sheet" Is used for
formalizing the calculation of the rate of variable cost,
and at the bottom of the page space Is provided for showing
this rate.
Of course this rate Is uniform at all levels
of activity, so there Is no necessity for a columnar
spread te develop costs by various outputs as were needed
In the case of semi-variable costs.
Only two items of In­
formation are needed In the case of the variable costs the
119
unit of measure and the rate.
The type of budget illustrated for foremen and floor­
boys is duplicated for each variable and semi-variable
cost at all activity levels for each cost in each depart­
ment of the plant.
The firm is then in an excellent
position to exercise rigid control over all costs at
any level of output.
Furthermore such a budget plan pro­
vides every item of Information necessary for a complete,
accurate determination of the differential cost of any
proposal which might be made.
Whether the proposal is in
terms of units presently produced or in terms of entirely
new units, whether it affects the entire plant or only
one department— whatever the proposal, a quick and accurate
differential cost determination can be made.
For example,
if the proposal requires operating the molding department
for six-hundred machine hours when the department is now
operating only 300 hours, it is quickly apparent that the
total foremen and floorboys* costs will Increase from
$309*40 to $567*80, or a differential cost of $258*40.
A
similar calculation for each cost in each department of
the plant will quickly produce the total differential cost
applicable to the proposal.
A comparison of this differ­
ential cost with the differential revenue Involved will
reveal whether the proposal is profitable--that is, whether
it will add marginal profit toward the coverage of the
120
firm's pool of fixed costs.
So far we have been dealing with the specific determi­
nation of differential costs for purposes of special cost
studies.
More recently a few forward-thinking cost
accountants have raised the question of applying the prin­
ciples of differential costs to the regular costing of
all units and to routine accounting and reporting.
The reasoning is essentially this: a firm is already
producing 100,000 units of product.
It is decided now to
produce an additional 10,000 units.
?he differential cost
approach would argue that the only costs applicable to the
10,000 units are those additional costs incurred directly
as a result of producing these units.
Why isn't it valid
then to reason that the costs applicable to any unit, be it
the first or the 100,00pth, are only those costs which can
be directly identified as having been incurred as a result
of producing that unit?
In other words, this plan would
charge units of production with ohly the variable costs
and exclude from cost of units manufactured any and all
fixed costs.
This production, charged with only the
variable costs, would be carried through to the balance
sheet and the income statement in this manner.
According­
ly, the plan has been referred to occasionally as "the elim­
ination of fixed costs from inventory," or the "direct
costing plan."
121
In addition to the underlying differential cost con­
cept there is one further theoretical aspect of this pro­
posal which should receive some consideration.
We have
already attempted to establish the theoretical justifi­
cation for Identifying only differential costs with units
of product for managerial decision purposes.
However if
all fixed costs are completely eliminated from all pro­
duction, what disposition is to be made of fixed charges?
Those advocating this approach find the answer in carrylng all fixed charges directly to the income statement In
the period In which incurred.
Not only do the advocates of this plan find theoretical
justification for It, but they see In this approach an
answer to the difficulties which arise In presenting Idle
capacity variances In the Income statement as outlined
first by Jonathan Harris1 and summarized here in Chapter
4.2
Figure 11 presents the same basic data that was used
in Figure 4.
In Figure 4 however the old approach was
used, wherein fixed overhead costs were spread over units
of product by means of a predetermined or standard over­
head rate.
The determination of such a rate necessitated
the use of some sort of normal capacity.
1 Harris, on. clt.
2
.p p . 501-2.
p. 81.
Then when
Basic datat
Standard cost: (per unit)
Direct material and labor $1.00
Variable factory expense
.15
Total standard
differential cost
$1.15
Sales price per unit
$2.UU
(Note:
First
Units produced
Units sold
Sales
Standard differential cost of sales
Standard margin
Variances*
Actual margin
Selling and administrative expenses
Fixed factory expenses
Total
Net profit
300.000
300.000
Fixed factory overhead, at any
production level, amounts to
$420,000 per year or $105,000
per quarter.)
Second
Third
.Quarter
Fourth
Quarter
280,000
300,000
300,000
350,000
280,000
270,000
barter
.
Year
1 , 230,000
1,150,000
$600,000 $600,000 *560,000 *5+0,000
i p o
345.000 122.000 .3 1 0 .goo
*255,000 $255,000 *238,000 *229,500
0
- 0- 0-0*255,000 *255,000 *238,000 *229,500
* 90,000 * 90,000 * 90,000 * 90,000
*2, 300,000
105.000
420.000
■
105.000
1.122.500
t 977,500
0
- -
*
105.000
*
977,500
* 360,000
THO'l'O'Oo
♦there were assumed to be no price or efficiency variances, and there is no
idle capacity variance with this treatment of fixed factory overhead.
Figure 11. Differential cost approach to the income statement with varying
units of production. (To be compared with Figure 4, page 81).
(Adapted from an unpublished paper presented by I. Wayne Keller,
Assistant Controller of The Armstrong Cork Co., before the
Midwest Cost Conference, National Association of Cost Account­
ants, Indianapolis, Indiana, April 4, 1952.)
H
FO
production varied from this normal, some unused overhead
cost (idle capacity variance) resulted which was thrown
into the Income statement and which distorted month to
month comparisons.
In Figure 11 the fixed portion of over­
head cost has been eliminated from cost of units produced
or sold and is carried directly to the Income statement.
This amounts to $105,000 every quarter whether any pro­
duction takes place or not.
The balance of the overhead
cost is the variable, which behaves with respect to units
produced in essentially the same manner as direct labor
and material cost.
If production takes place,the cost is
incurred and taken Into the Inventory value; if no pro­
duction occurs, neither does the cost and there Is no
problem of unused capacity.
Since sales are the same In
the first two quarters, net profit for the two periods
is the same regardless of the fact that production in the
second quarter had declined.
With sales declining in the
third and fourth quarters profits decline, even though
production is on the increase.
This is quite a differ­
ent picture than that presented in Figure 4 covering the
same data.
The proponents of this treatment of handling fixed
overhead costs feel that they have theoretical justifica­
tion for this approach.
One writer says; "According to the
marginal approach, fixed costs cannot be considered costs
124
of manufacturing units of product because of their nature;
and, therefore, they should not be applied to these units*
In the first place, there are the shut-down costs such as
depreciation, certain taxes, rentals, certain insurance
and salaries, etc., which will continue to be Incurred
if no production at all takes place.
Therefore, if they
are the costs of not producing goods, how can they logically
also be called costs of producing goods when production
actually does take place.
These costs are not affected by
any decision to resume production, and the assumption of
the accountant that they are being 'converted1 into the
form of produced units, when he applies them to these
units, Is inconsistent and disregards the inherent
nature of these costs.
These shut-down costs and all other
fixed costs accrue strictly on a time basis and the ser­
vices purchased when these costs are incurred are being
consumed with every passing second.
Once this second has
passed, the services consumed are Irrevocably lost, whether
1
or not the company has benefited therefrom."
The proponents of this differential costing for the
Income statement make much of the fact that these fixed
costs are time costs and attempt to justify the procedure
accordingly.
However It should be pointed out that the
1 Sapega, Andrew S., "More Useful Accounting for
Indirect Costs", Bulletin
the NatJ-opaj Association o£
Cost
tantsT September. 1951, p. 19.
procedure since It eliminates fixed costs from cost of
production will result In greatly reduced Inventory values
In the balance sheet*
Some writers have attempted to
minimize this aspect of the plan, pointing to the effect
which LIFO has already had upon Inventory values*
The
point Is not this so much as it is a question of the use
which Is to be made of the statements.
More and more
accountants are recognizing the fact that the way in which
statements are prepared must depend to some extent upon
the use which Is to be made of them*
This Is the answer
to the question of the effect of the differential approach
to inventory Valuation.
The differential technique has
merit from the standpoint of most managerial decisions,
and the under-valuation of the Inventory would probably
be of little consequence from the managerial point of
view*
Adjustment would have to be made In considering the
working capital position.
However the value to be gained
from the Improved Income statement for managerial purposes
might outweigh the disadvantages.
From the viewpoint of
the stockholders, creditors and particularly the banker
who may be extending short-term credit, a different report
should probably be prepared which would give more careful
consideration to Inventory values.
To the stockholder who
essentially has a long-run point of view, spreading of
total costs, Including fixed, to all units of production
126
may be more advantageous.
However It has been conceded
from the outset that differential costs were a tool for
management's use In viewing the short-run, and It Is In
this sense that the differential Income statement is justi­
fied.
Further logic and advantages of the differential
Income statement can be seen where the statement is prepared
comparatively by products.
is illustrative.
Figure 12 on the following page
I’he only costs which are identified with
products are the differential costs, those costs directly
applicable to the particular products.
They are the costs
which would not have been Incurred if the product had not
been produced.
The statement deducts these direct costs
from the revenue which they produced, the remainder if any
being that product's contribution to the coverage of fixed
costs and a profit.
Chapter 4 outlined the difficulties which arise in
attempting to allocate fixed costs to product and questioned
the reliability of the results.
Figure 12 merely eliminates
all these difficulties and provides a statement which may
be more meaningful.
If the fixed costs in Figure 12 were
allocated to products on some arbitrary basis, it is con­
ceivable that product C might result in a loss since its
differential margin of profit is lower than in the case of
the other products.
Whether or not this product would
Total
Sales
Product Product Product Product
C
D
4 , A _ x _B
$600,000 $ £0,000 #200,000 $ 225,000 $12^,000
Differential cost of goods sold
(material, direct labor and all
other directly variable costs)
_3+5.,.ooo _ 24 JOO
Contribution to the coverage of
fixed costs
#255.000 # 25,500 SIQ2.,.0P.Q # 67.500 LiP.,,Q0P
...
Rate of contribution based on sales
Selling and Administrative expenses
Fixed factory overhead
Total
Net profit
Figure 12,
51%
98.000
51%
157.500
305#
$ 90,000
105.000
#195.000
$ 60.000
Comparative differential cost income statement by products.
65.000
48#
128
result In a loss, and how much that loss would be, would
depend entirely upon what arbitrary bases were chosen for
making the allocations.
Furthermore as was noted In
Chapter 3, If the product Is marketed competitively, some
questions might be raised as to the usefulness of the
profit or loss figure resulting from such a calculation.
Since selling price cannot be adjusted, the most signifi­
cant aspect about product C Is that It Is covering Its outof-pocket costs and providing $67*500 toward the coverage
of the pool of fixed costs and profit.
The greater the
degree of monopoly which exists In marketing product C,
the more value which may be found In the total cost alloca­
tion.
In using the differential Income statement classified
by products, management will undoubtedly develop some
Mrule-of-thumb*1 with respect to the ratio of differential
margin of profit to sales for each product and in total.
However assuming conditions of competition, there would be
no control over this ratio; and management could not be
assured a net profit merely by maintaining a particular
ratio for given products.
Net profit Is the result of
a pooling and cannot be provided by any one unit or product
or product class.
In this discussion of the presentation of the differ­
ential Income statement, one complicating factor has thus
129
far been Ignored: what treatment Is given to the semi­
variable costs in this type of statement?
In the pre­
ceding discussion, costs were simply referred to as
variable or fixed— variable deducted directly from revenue
by classes of sales, and fixed deducted below in total only*
Where in all this are the semi-variable or semi-fixed costs,
those which progress in a step-like fashion as volume in­
creases?
It is these semi-variable costs which gave us difficul­
ty in applying differential costs to special cost studies;
and it is the semi-variable costs which present the diffi­
culty now in applying differentials to the costing and
reporting of total production and sales.
If all costs
could be classified as either strictly variable or strictly
fixed, the situation would be greatly simplified.
unfortunately this is not the case.
But
Quite to the contrary,
over wide ranges of production many costs are semivariable •
There appear to be several possible approaches to
treatment of semi-variable costs when applied to the costing
of total operations.
One approach would treat them as
entirely fixed, showing them in total only.
Another approach
would sheer them entirely as variable and deduct them as
differential costs by revenue classes.
A third possibil­
ity would be to show some of them as fixed and others as
130
variable, depending upon the degree of variability of each.
Most of the few writers who have discussed this sub­
ject think in terms of the first approach.
They would treat
as variable only those costs which are purely variable—
those which vary directly in proportion to output at all
levels of output.
Semi-variable costs are classed as
fixed, in fact no distinction is made between the two in
the income statement. One writer, for example, says:
"There is one more definition of semi-variable cost which
is in use today.
I refer to those costs which are subject
to variation in steps at certain levels of production between
zero and maximum for any individual plant.
Such a repre­
sentation may be accurate; but practically speaking the
operations of a going concern do not vary over all possible
levels of productive activity between the absolute minimum
and the absolute maximum, especially within any one fiscal
period.
The executive and the accountant are generally
concerned with the actual range of productivity expected
and experienced.
Within this range most semi-variable
costs such as supervision and service department costs
tend to be fixed.
I admit that they are subject to varia­
tion when we consider all possible levels of productivity,
but within those surroundings in which the executive and
the accountant work and make their decisions— the actual
range of productivity experienced— semi-variable costs act
131
1
no differently than fixed costs#”
Another author prepares a differential income state­
ment in the exact manner of that in Figure 12 but shows a
breakdown of the costs Included in "fixed factory over­
head*”
It includes "salaries, rents, wages (caretakers, et.
cetera), rates, heating and lighting, accountancy charges,
insurance, postage, miscellaneous, maintenance, and depreelation."
Obviously, mapy semi-variable costs are Included
in this classification.
To include all semi-variable costs as fixed would be
the most simple procedure.
Particularly where production
is complex and a variety of products are being manufactured,
some difficulties may be encountered in identifying semivariable costs with products.
Consequently it would be
the simple approach to exclude such costs from product
costs and Include them as fixed costs, in total only.
An accounting system designed to produce this type of
information would likewise be less complex.
Accounts for
semi-variable costs would be kept on a departmental basis;
but beyond this, no further disposition of the cost to
products would be made.
The directly variable costs would
be allocated to product on a per-unit or per-pound, or perdlrect-labor or per-machlne-hour basis.
Since these costs
1 Sapega, ibid., p. 19*
2
Lawrence & Humphreys, op. cit.. p. 55.
132
are strictly variable no problems would arise in assigning
them to product, either on an actual, historical basis or
upon the basis of a standard or pre-determined rate.
The simplicity of operation of this plan is one of
the most important points in its favor.
If there is no
need to identify semi-variable costs by products or in
terms of other plant activity, then certainly it should
not be done; and according to Mr. Sapega1, there is no need.
However a number of the executives Interviewed expressed
a different opinion, and evidenced a desire for methods of
assigning the semi-variable costs to products.
A point In Mr. Sapega's discussion is probably the
clue to the difficulty here.
H© says that the reason that
semi-variable costs should be treated as purely fixed is
that, within reasonable expectations, there is little
fluctuation in levels of production, and accordingly
little change In the so-called semi-variable costs.
It
has been observed earlier in this discussion that within
narrow ranges of volume fluctuations, there would be little
change in these costs.
It appears then that where a firm experienced little
fluctuation in productive volume, treatment of semi-variable
costs as purely fixed would be justified as well as practi­
cal.
But differential costs have their greatest usefulness
^
P* 130.
133
in connection with problems of fluctuation volume; and as
one executive stated, it doesn't take much change in volume
before changes in semi-variable costs make themselves
felt.
Referring to Figure 12, product B had a differential
cost of $98,000.
If this represented the sale of 49,000
units and if all of the costs are strictly variable costs,
then each unit has a strictly variable cost of $2 per unit*
Now if the firm never fluctuates only within very narrow
limits, it may not be necessary to know anything further
about B except the variable cost of $2 per unit.
But If
the production of product B should expand moderately, it
is reasonable to expect that an added payroll clerk should
have to be hired or an extra mechanic would be added to
service machinery,or somewhere in the plant some semivariable cost would step up.
Where such fluctuations in volume occur, it is clear
that costs other than the strictly variable should be
identified with products.
It was seen earlier in this
chapter that carefully prepared budgets of semi-variable
costs will provide the information necessary to prepare
speelal cost studies with respect to specific proposals
affecting particular products.
But how can semi-variable
costs be identified with product as a regular accounting
routine?
Assume that products A,B,C and D are all processed
In one month In department M in a type of operation which
can be measured In terms of direct labor hours.
Assume
further that the department can be operated up to 160
hours per month with one foreman at a cost of $4-00, but
operation of between 160 and 320 hours requires two fore­
men at a cost of $800.
When the general combined output
of all products Increases beyond the 160 hours, which prod­
uct should be charged with the added $400 cost?
If the total
cost Is divided by the hours expended on all products, it
is clear that at the l6l-hour level we would have one
rate; while at the 320-hour level there would be an en­
tirely different rate.
If a predetermined or budgeted
figure for foremanshlp cost per hour is to be determined,
it is obvious that some assumption must be made as to
level of output--probably "normal” capacity— and the dif­
ficulties growing out of this concept are well known.
The answer to this problem was suggested by a tech­
nique in the system which was being developed in one of the
plants visited.
The effect of the technique was to combine
all of the semi-variable costs into one class— in effect
average them together— so that when taken together they
would no longer progress in a step-like fashion;but the
steps would be smoothed out, and in total a purely variable
cost would result.
In other words if only one semi-variable
135
cost Is considered, it presents the difficulty of a step­
like progression; but when many semi-variable costs are
totaled together, the steps will be smoothed out.
Figure 13, on the following page, shows budgeted
amounts of individual semi-variable costs over a wide
range of production.
Individually they appear in the
traditional step-like fashion.
The unit prices of the
individual semi-variable costs fluctuate widely as the
output may change and the cost does not.
For example,
the semi-variable unit cost of cost A fluctuates from a
low of 27 cents at one level to 40£ents at another level.
The unit price of cost £ is completely doubled at the
1,000 unit level as compared with the 2,000 unit level of
output.
However by totaling all of the semi-variable costs
and taking an average at each level, the fluctuations in
unit price are smoothed out.
In the illustration the unit
price fluctuates from $1*17 to $1.26; but by making certain
refinements in the calculation, the average might remain
even more constant.
A greater number of semi-variable costs
are probably found in most departments, bringing more
numbers into the average; and the budgeted figures may be
set up at closer Intervals than was done in Figure 13.
The average of the unit prices developed in Figure 13—
approximately $1.20 per unit— would be a close approxima­
tion of the variability of all semi-variable costs combined.
136
Semi-variable
cost
Units (or Hours or some other base)
1.000 1.500 2.000 2.500 3.000 _3_,500
$
A
B
C
D
E
F
4-00 $
50
200
300
50
200
400 $
100
400
600
50
200
800 $
100
400
600
50
400
800 $1,200 $1,200
150
800
900
100
400
150
800
900
100
400
200
1,200
1,200
100
400
$1,200
#,1*Z1Q
$2,350 $3^150 $3.550 §±*300
Total semivariable
unit cost
$ 1.20
§.JU1Z
$ 1.18 $ 1.26
00
H
•
H
Total
Figure 13. Budgeted semi-variable costs
at various output levels.
§-1,23
Another way of calculating an average semi-variable
cost figure Is by use of a scattergram,
This technique Is
Illustrated In Figure 14 on the following page.
The total
costs, exclusive of raw materials, of operating a depart­
ment are plotted graphically as represented by the dots
on the chart.
Then by the statistical method of least
squares, a line is plotted
which is in effect the average
of the poftits
representing total cost. This line— AB in
Figure 14— is
projected to the Y axis. The point at which
it meets the Y axis would represent the purely fixed or
shut-down costs of the firm.
In other words in Figure 11
if units produced are zero, the total cost line stands at
$2,000.
firm.
This would then represent the fixed cost of the
By subtracting the fixed costs, so-determined, from
the total cost at each output level, the balance would
represent the variable and semi-variable costd.
At this point, two procedures are available.
The
strictly variable costs such as direct labor could now
be subtracted.
This would leave a balance representing
only the semi-variable cost.
Figure 15, on page 139,
illustrates how this might be done.
First,the AD line is
drawn horizontally from the Y axis at the point at which
it is bisected by the total cost line, AB.
This area
below line AD represents the fixed cost of the firm.
Next, the purely variable cost is plotted above the fixed
138
10
Y
H
10
Units (Thousands)
Figure 14. Scattergram used to determine
rate of variability of semi-variable costs*
139
10-
(Thousands)
B
Dollars
Semi-variable
Variable
Fixed
1
2
4
6
Units (Thousands)
Figure 15. Plotting fixed and variable
costs In order to calculate semi-variable
costs.
10
140
cost line.
This was assumed to be 2 % per unit In Figure
15, and the total of this variable cost above the fixed
is represented by line AC.
Now the remaining difference
in the area BAC represents the combined semi-variable
cost at any given level of output.
This difference can
now be measured and resolved In terms of cost per unit for
purposes of further accounting application.
An alternative approach might be used, provided that
direct labor hours are used as a basis for measuring
activity In the department.
Since cost of direct labor Is
measured In terms of hours, if other variable and semivariable costs can also be measured In terms of hours
there would be no particular need for separating the two;
and one total expense rate could be developed to include
both variable and semi-variable expenses.
In this case
the X axis on the scattergram would be stated In terms of
direct labor hours, and the total costs plotted would be
for the various activity levels in terms of direct labor
hours.
The fixed cost line would be projected In the
same manner; and the remaining area would represent the
total variable and semi-variable cost, all In terms of
direct labor hours.
This total can then be measured and
resolved Into terms of cost per direct labor hour.
All of this is designed to provide a rate which will
represent the average cost of the combined semi-variable
141
expenses at any and all volume levels.
This averaging
technique seems justified, particularly where we are
thinking in terms of fairly Important changes In volume*
Under such circumstances, semi-variable costs become
fundamentally variable; and the average is the only
practical means for handling them.
It should be emphasized that this average semlvariable cost rate does not repeat the errors of the
average factory overhead figure which caused so much dif­
ficulty.
In order to calculate the factory overhead rate
(which Included fixed as well as semi-variable) some volume
level had to be assumed— usually normal capacity.
Then the
rate had little validity for other volume levels and led
to the many other difficulties outlined In Chapter, 4.
The average semi-variable cost rate Is not thus de­
pendent upon a volume assumption.
It is valid at every
volume level if the average has been worked out carefully*
Thus In Figure 10, the average is approximately $1*20 per
unit of product, and this may be applied at any volume
level*
The use of the concept is limited to the framework
of the assumptions upon which it is based.
For example
If one unit of output is added In a department, semivariable costs will not necessarily go up; by $1*26; but
If 500 units are added, semi-variable cost will tend to
142
go up by approximately $600 (500 x $1.20).
This is an
average, and some fluctuation may be expected.
Further­
more, not all semi-variable costs can be expected to in­
crease; but while some increase and others remain con­
stant, the average fluctuation will amount to $600.
In summary then, in preparing a differential type of
income statement (Figure 12), semi-variable costs may all
be classified as fixed.
This would be the more simple
approach and is Justified if only very minor fluctuations
in volume occur.
Where more noticeable changes in volume
are common, the changes in the semi-variable costs become
of greater importance and should be included in differential
cost.
This may be done on the basis of an average rate
per unit (hour, etc.) for all semi-variable costs within
a department.
Most of the preceding discussion of an average semivariable rate was in terms of budgeted figures and costs.
It should be pointed out that the technique has equal
applicability in the treatment of actual historical semi­
variable costs.
Actual semi-variable costs may be totaled
at the end of the period and divided by units produced in
order to arrive at the average semi-variable cost per unit
(hour, etc.).
This rate may then be applied to production
to arrive at a differential cost of goods manufactured for
purposes of inventory valuation and differential cost of
143
sales for purposes of the Income statement.
Although the technique may be used In historical cost
determinations. Its real value lies In the determination
of standards, budgeting and planning.
By carefully budget­
ing each semi-variable cost In accordance with the methods
outlined earlier In this chapter, the scattergram can then
be prepared upon the basis of budgeted figures; and the
semi-variable rate per unit (hour, etc.) becomes a standard
rate.
This standard rate would have two distinct advan­
tages and uses.
First, it can be applied to production
to arrive at standard differential cost of sales which can
then be compared with actual costs, and variances may be
investigated.
Secondly, the rate may be used as a quick
means of providing management with cost estimates for
particular proposals regarding expansion or contraction
of volume.
Earlier in this chapter, there was a discussion of the
use of detailed budgets of seml-varlable costs for pur­
poses of special differential cost studies.
Now, by com­
puting average semi-variable departmental expense rates, It
Is possible to provide a quick means of arriving at a
rough approximation of the differential cost of particular
proposals.
Thus If the average seml-varlable expense rate
In a particular department is $1.20 per hour and It Is
proposed to operate the department an added 1000 hours,
144
It would be safe to estimate that the differential semlvariable cost of the proposal would be $1,200.
Reference
to specific budgets for each of the seml-varlable costs
within the department might disclose that the figure should
be slightly more or slightly less, but the average rate
will suffice as a quick, handy guide to proposed actions.
The following example will further Illustrate the
use of standard variable expense rates in special cost
studies.
Assume that a firm produces five products, iden­
tified as A,B,C,D and E.
These products are manufactured
in one process (department) In which all activity can be
measured In terms of direct labor hours.
Standards for the
five products have been established as shown In Figure 16.
since all of the activity in the department can be measured
in terms of direct labor hours, all variable, seml-varlable
and direct labor costs are combined Into one rate ($3) per
direct labor hour, as discussed on page 140.
Proposed Increases or decreases in production of any
units can readily be calculated In terms of differential
cost and compared with differential revenue.
Assume that
present selling prices and volume are as follows*
14-5
Present
Product
Unit Selling
________ Price
Present
Volume
(Units)
Present
Total Sales
Volume
A
$35
5,000
$175,000
B
$29
8,000
232,000
C
$20
6,000
120,000
D
$30
5,000
150,000
E
$19
3,000
Total
Proposal #1.
...
52.+QSQ.
ft7^4rOOP
It Is now proposed to reduce the selling
price of product A In order to secure an increase In volume.
Careful market surveys indicate that if the unit selling
price of product A were reduced to $32 per unit, a total
of 7,pOO units could be sold.
The Controller Is asked
to prepare a report on the profitableness of this proposal.
Differential revenues
Proposed revenue (7*000 units @ $32)
$224,000
Present revenue (5*000 units @ $35)
Differential revenue
175.000
$ 49,000
Differential cost* 2,000 units @ $23
Differential profit resulting
from the proposal
Proposal #2.
4 6 T000
$
^.000
It Is noted that the above proposal would
Involve added production of 2,000 units; and since each unit
of A requires 6 hours of productive time, the total proposal
would require an additional 12,000 hours.
Assume that the
Standard
Products
Standard Cost Per
A
B
C____ ______ D___________ B
Unit of Unit of Unitsodf
Units of
Units of
Units of
Units of
Measure Measure Measure Cost Measure Cost Measure Cost Measure Cost Measure Cost
Material
Lb.
$1.
5
$5.
7
$7.
$
$8.
3
$3.
2
$2.
Variable
and semivariable
expense
Hour
$3#
6
18.
4
2^.
^
6.
8
24*
4
12.
Total unit standard
differential cost
$23.
$19»
114•
$27.
$14.
Figure 16. Standard Differential Costs By Units of Product.
p
147
plant is already producing at top capacity, and in order to
increase production of A, a decrease must be made in the
production of some other units.
Figure 17 shows the cal­
culation of the effect of a reduction of 12,000 hours in
each of the other four products produced.
It is clear
from this calculation that a reduction of 12,000 hours in
the production of any of these four products would result
in a greater decrease in differential profit than the
increase which would result from the added units of Product
A.
The smallest reduction In total differential profit
would occur in product D; but even in this case, the firm
would lose $4,500 of differential profit and gain only
$3,000.
Accordingly the proposal for an Increase in the
production of product A should be abandoned.
Proposal # 3 1
> Another type of proposal might Involve
the abandonment of one product line and replacement by
another product line.
Under present circumstances the
various products are contributing to the coverage of fixed
costs as shown in column 6 of Figure 18.
From this it is apparent that products P and £ are
making the smallest contribution toward coverage of the
firm's fixed costs— namely $15*000.
However, the con­
tribution of product D Is only $3 per unit while product
£ is $5 per unit.
Since product D requires eight direct
labor hours per unit, a total of 40,000 direct labor hours
(2)
Units
Produced
Standard In 12,000
Hours
Hours
Per Unit 12.000-Col,1
(1)
Product
(3)
(4)
(6)
Decrease In
Differential
Total
Unit
Unit
Profit
Differential
Selling Differential
Per Unit
Profit
Price
Cost
Col.3-Col.4 Col.2 x Col.1)
(5)
S
4
3,00 0
$29
$19
$10
$30,000
c
2
6,000
20
14
6
36,000
D
8
1,500
30
27
3
4,500
E
4
3,000
19
14
5
15,000
Figure 17.
Calculation of the effect upon differential profit of a decrease
of 12,000 hours in the production of each of four products.
(1)
(2)
Unit
Selling
Price
Initial
Standard
Differential
Cost
(3)
Present
Volume
(4)
Present
Total
Sales
Revenue
(1x3)
(5)
(6)
Present Total
Total
Differential Differential
Cost
Profit
_(2x3)
(4-5)
(7)
Unit
Differential
Profit
(1-2)
A
•35
•23
5,000
•175,000
•115,000
$60,000
$12
B
29
19
8,000
232,000
152,000
80,000
10
C
20
14
6,000
120,000
84,000
36,000
6
D
30
27
5,000
150,000
135,000
15,000
3
E
19
14
3,000
57,000
42,000
15,000
5
Figure 18.
Calculation of contribution to coverage of firms fixed costs
(differential profit;.
149
150
are devoted to its production (8 hrs. x 5*000 units).
E
requires only four hours per unit or a total of 12,000
direct labor hours (4- hrs. x 3,000 units).
Accordingly it is proposed that product X be sub­
stituted for product D.
A careful market survey is con­
ducted, and it is determined that a maximum of 15*000
units of X can be sold at a selling price of $28 each.
Engineering estimates determine that the standard cost of
producing a unit of X would be as followss
Material, 20 lbs.
@ $1
Variable and semi-variable
expense* 2 hrs. @ $3
Total
$20
6
$26
This provides a differential profit of only $2 per
unit— $1 less per unit than was provided by product D.
However since 15*000 units of X can be sold, total differ­
ential profit will amount to $ 30,000 (15*000 units x $2).
Since production and sale of product D is providing differ­
ential profit of only $15*000, it would be beneficial to
discontinue product D and adopt product X.
Furthermore the discontinuance of product D will
release 40,000 direct labor hours, while product X, re­
quiring only two hours per unit, will utilize only 30,000
direct labor hours, leaving 10,000 hours of capacity
available for other uses.
There is one further aspect about the scattergram
151
technique described earlier.
The total cost lines in the
scattergrams in Figure 14 and 15 were represented as
straight lines, whereas it was pointed out earlier that
economists conceive of the total cost line as curved
(Figure 7).
This raises a question as to whether or not,
in preparing the scattergram, a curve might not result from
the joining of the plotted total cost points, due to the
principle of non-proportional returns*
This question was
raised with the controller in the only firm found to be
using this scattergram technique.
He was plotting actual,
historical, total costs; and his experience to date had
been limited to a rather narrow range of volume*
Therefore
he had attempted only the plotting of a straight line.
Statistical techniques are available, however, to test a
series of data to see whether it is best fitted for a
curve or a straight line*
1
If the plotted points conform
best to a curve, further statistical techniques are avallable to describe this curve mathematically.
This in
effect would give us a semi-variable expense rate which
would not be absolutely constant, but which would increase
in rate when the point was reached where inefficiencies
develop*
Croxton. Frederick E., and Cowden, Dudley J
. Statistics. New Yorks Prentice-Hall, Inc.,
2 Ibid. Chapters 15 and 16*
152
Chapter 6
Non-manufacturing Uses of
Differential Cost Accounting
The discussion in the preceding chapters was chiefly
confined to the manufacturing enterprise.
While the dif­
ferential cost approach is of great value in this area of
costing, it is of equal value in other areas of business
and commercial activities.
Several of the more important
of the non-manufacturlng uses will he discussed In order
to demonstrate the wide applicability of the differential
cost technique.
Lawrence and Humphreys says
"The benefits
of marginal costing, however, can be enjoyed by any com­
mercial enterprise, by the wholesaler and even by the
retailer, and are as necessary to them as to the manufac1
turner•"
The differential technique can be of great assistance
in the field of distribution cost accounting.
In discus­
sions of distribution costing, it is usually observed that
this field has not had the attention that has been given
manufacturing costs.
This was well supported by the com­
panies visited in this study.
Very few of the companies
in the group had pursued distribution costing to any great
extent.
One company had a rather complete system of dis­
tribution costing; several others had a knowledge of major
items of distribution costs, while others had done practi­
cally no work in this area.
■^■ Lawrence
& Humphreys,
op
.-Sit.,
P. 9.
There are undoubtedly a number of factors which have
contributed to the reluctance of co3t accountants to
develop this field.
It Is well recognized as an Important
area for cost analysis and control, but It is also recog­
nized that It Is a complex field of accounting.
In man­
ufacturing cost accounting, there Is usually one final
objective— costs by units of product.
It Is true that
costs are accumulated by object and by departments, and that
cost, control is effected on this basis.
However It is also
true that departmental costs are an Intermediary step
toward the final objective of product costs.
In distri­
bution costing however, there may be many cost objectives.
Distribution costs by products may be one objective, costs
by territories may be another, costs by salesmen, costs
by order size, costs by channels df distribution, costs
by customers or classes of customers— all of these may be
the objective of a distribution cost accounting system.
Bach objective requires separate study and cost procedures.
In addition to these complexities, there Is the fact
that selling and administrative expenses Include a large
fixed element.
A failure to understand the nature of
fixed costs and unrefined accounting techniques for handling
them may be factors which have retarded the development
of distribution cost accounting.
Although some cost accountants have recognized the
154
advantage of differentials in distribution costing, the
usual approach is a total cost approach.
That is in any
cost allocation, all costs are allocated, fixed, semivariable and variable.
First, selling and administrative expenses are classi­
fied by functions such as warehousing, sales promotion,
direct selling, travel expenses, order filling, delivery,
credit and collection, and billing and accounts receivable.
These functions, for accounting purposes, correspond
roughly to the departmental classifications used in man­
ufacturing cost accounting.
Such classifications are
absolutely necessary in order to establish the cost of
functions or services being performed.
In manufacturing
accounting, these service costs are then distributed to
the products benefited or the territories benefited or the
customer class benefited or to whatever the objective of
the classification may be.
Essentially then,i|anufacturlng
cost accounting and distribution cost accounting are funda­
mentally alike.
In classifying costs by functions as when classifying
them by departments, some functional costs are variable,
some semi-variable and others are fixed.
The importance
of this mixed nature of functional costs has been overlooked
in distribution cost accounting.
In many Instances the
entire functional cost has been treated as though it
155
were variable.
In other words, the same difficulties are
found here as were found in manufacturing accounting, where
departmental overhead rates were developed including
variable, semi-variable and fixed factory overhead.
Figure 19, on the following page, is typical of the
way in which functional costs are allocated in distribu­
tion cost analyses.
The warehousing and packaging function
for example would Include some purely variable costs,
such as packing containers and supplies.
It would include
some semi-variable costs such as workmen's salaries.
It
would Include some fixed or sunk costs such as building
depreciation, taxes and insurance.
Nevertheless this cost
is stated as $.03 per unit handled and allocated to ter­
ritories accordingly.
The final result of this procedure is to carry all
fixed costs of the firm to the three territories on some
arbitrary base.
When no better base is available, costs
are prorated on the basis of the value of sales in each
territory, as in the case of administrative expenses.
In regard to such cost techniques, Carl Devine has
said:
"While the need for distribution cost control Is
unquestioned, some accountants have undoubtedly become
over-enthusiastic about the possibilities of such proced­
ures.
Does the fact that the New England Division
operates at a loss mean that the division should be
Cost
Basis of cost distribution
Unit of
distribution
Number
Virginia
Units Cost
Maryland
Units
Cost
36,000 $1,080
26,000 $2,780
$1,200
I;, 000
2.00
8,000
1,800
3^600
1,200
2,1*00
1,000
2,000
50,000
..06
3,000
20,000
1,200
15,000
900
15,000
900
I*,000
.20
800
1,800
360
1,200
21*0
1,000
200
1*0,000
.15
6,000
15,000
2,250
15,000
2,250
10,000
1,500
15.000
.02
300
6,000
120
5,000
100
1*,000
80
2.000
.05
100
1,000
50
700
35
300
15
102,000
$ .03 $3,060
-
3,000
**
o
8
Total selling and
administrative
West Virginia
Units Cost
%
Warehousing and
packaging
Hundred weight
Sales salaries Number of
calls
Salesmen'8
traveling
Miles
Sales offl.ce
Number of
calls
expense
Direct mail ad­
vertising
Units mailed
Invoicing and
billing
Lines invoiced
Collection
Remittances
handled
General ado&nistration
Sales
Cost
Total
Cost
mm
$2i*,26G
1,200
-
$9,980
1,000
-
$8,005
ligure 19. Allocation of total distribution and administrative
expense to territories
(Adapted from Devine, Cost Accounting & Analysis, p. 5Uu
New York* Macmillan Company, 1950.)
800
$6,275
159
abandoned?
If product A exhibits chronic losses, should
the product be discontinued?
Does the apportionment of
central warehousing costs to sales territories aid in the
control of such costs?
ly in the negative.
In each case the answer is certain­
In view of these obvious limitations,
it is not surprising that many businessmen, economists,
and accountants have been discouraged with the results of
systems which call for Intricate assignments of fixed
costs.
New tools must be forged and added to those al1
ready in existence.'1
An elaboration of the need for new tools can be drawn
from Figure 19*
Assume that sales in Virginia amounted
to #30,000 and that total cost of sales in this territory
amounted to $23,000.
This would provide a gross profit
of $7)000 and a net loss of $1,005 In this territory after
deducting the distribution and administrative expenses
of $8,005loss?
Just what is the significance of the $1,005
In the first place, since some of the bases for
allocating costs to this territory were purely arbitrary,
the final figure is arbitrary.
Furthermore does the loss
figure Indicate that this territory should be dropped?
Here again the answer is not found in this total cost
allocation.
The question is one of differential costs.
If the revenue from the Virginia territory is sufficient
1 Devine, Carl Thomas, Cggt Accounting and Analysis,
New Yorks Macmillan Company, 1950, p. 548.
158
to cover the differential costs applicable to that territory,
then it is contributing something toward the coverage of
the firm's pool of fixed costs and profit.
But this vital
information is not revealed by the type of cost calcula­
tion shown in Figure 19.
The differential approach would assign to territories
(or whatever cost analysis is being made) only the direct
costs Incurred in connection with that territory, or
stating it differently— those costs which would not be
incurred if the territory were discontinued.
Such a treat­
ment of distribution costs, along with the differential
treatment of manufacturing costs, would result in the
type of statement shown in Figure 20 on the following
page.
The accounting for and calculation of differential
costs of distribution will follow essentially the same pro­
cedures as differential cost accounting for manufacturing.
Cost accounts would be set up for each variable cost for
each function, just as wascdone by departments for manufac­
turing costs.
Fixed costs would be excluded from function­
al classifications.
The same problem would be faced here
with semi-variable costs as was found in manufacturing,
and the same alternative treatments are available.
All
semi-variable costs might be Included with the fixed.
This is the simple procedure and would find justification
159
Income Statement
for the month ended -- ------
Sale3
Total
Territory
#1
Territory
#2
Territory
#3
$100,000
$50,000
$30,000
$20,000
40.000
21.000
11.000
8.000
$ 60,000
$29,000
$19,000
$12,000
16.000
6.000
6.000
4.000
$ 44.000
$23,000
$13,000
$ 8.000
Differential cost of sales
Production margin
Differential cost of distri­
bution
Selling margin
-
Fixed expenses
Fixed factory expenses
$ 20,000
Fixed selling expenses
10,000
Fixed administrative ex­
penses
Total fixed ex­
penses
Net profit
8.000
$ 38.000
$
6.000
Figure 20. Income statement prepared to show differential
cost of sales and differential distribution costs•
1$0
where volume changes are slight*
Where wider fluctuations
in volume occur, a semi-variable expense rate should be
developed In accordance with the techniques outlined In
Chapter 5.
The variable expenses and the semi-variable
expenses, stated as a rate per unit of functional service
performed, would serve as a basis for the determination
of the variable cost of the function by products, territor­
ies, customers, etc*
Although cost accounting textbooks have discussed
standards for distribution costs, there seems to be little
evidence of the practical applications of distribution
1
standards In practice.
Such standards as have been
developed In textbooks have been based upon total cost.
Since total cost Includes the fixed, some assumption must
be made with respect to volume level— usually "normal"
capacity.
Thus In the Illustration used In Figure 19,
Devine develops a standard cost figure of $.03 per unit for
warehousing and packaging costs by assuming that 102,000
units Is normal capacity and that $3>060 Is the standard
cost for that capacity.
The difficulty to which such
reasoning leads was fully developed in Chapter 4 and will
not be re-stated again.
On the other hand, unit standard
rates developed for variable and seml-varlable distribution
1 There is no forgal evidence to be cited in support
of this contention, but it is based upon Impressions re­
ceived In the companies visited In connection with this
study as well as In other companies with which the author
Is familiar.
161
costs are not only theoretically justified, but they would
be useful for control purposes.
Another excellent example of the use of the differential
cost technique is found in the case of department store
accounting.
In fact differential costs have probably
received more attention in this area than in either manu­
facturing or distribution cost accounting.
The primary
objective of cost allocations in a department store is to
arrive at costs by departments.
allocations had been total costs.
Prior to 1934-, these cost
In other words, Included
in the cost of a particular department was not only the di­
rect costs Incurred by that department, but a full share
of such store-wide fixed costs as rent or building depre­
ciation, executive salaries, Insurance, taxes, etc.
In
1
one department store visited, where this type of plan
was still in use, they had arbitrarily determined that 26%
of the total "building occupancy" cost should be allocated
to first floor departments (it was a six-story building).
This cost was then further sub-divided between the first
floor departments on the basis of the relative floor space
•ccupled by each.
The Standard Expense Accounting Manual for Department
Stores and Specialty Stores sayss "...the Net Profit Plan
1 Referred to by the industry as the "Net Profit
Plan" since it arrives at a net profit for each department.
162
charges them (departments) with expense, over which they
have no direct control and by methods of distribution which
are not always true measures of departmental participation
1
or benefit*”
An example is cited to show the inequities
which may develop where executives' salaries are allocated
to departments on the basis of sales volumes
ments have been doing $100,000 a year volume.
”two depart­
It seems
entirely fair that each should have an equal amount of the
Indirect expense*
However, one year, one department begins
to slip in sales volume.
The general manager, publicity
man, merchandise manager, buyer, controller— all give a tre­
mendous amount of time and thought to the department, but
still its volume moves down to $50,000.
The other depart­
ment Increases its volume to $150,000 without anyone paying
much attention to it*
At the end of the year, this depart­
ment has prorated three times as much expenses as the
$50,000 department, in spite of the fact that more time
and expense went into the management of the $50,000 depart2
ment.”
Because of these disadvantages of the ”Net Profit
Plan” , Mr* Carlos B. Clark of the J* L* Hudson Company,
Detroit, in 1934 Introduced what he called the "Contribution
1 Controllers' Congress, National Retail Dry Goods
Association, Standard Expense Accounting Manual for Department Stores and Specialty Stores, 1950 Edition, p* 127*
2 Controllers' Congress,
P- 127*
163
Plan” for accounting for departmental operations.1
Un­
doubtedly this plan was original with Mr. Clark, illustrating
once again that persons in all walks of life do think
fundamentally in terms of margins, for this is merely the
differential cost approach by another name.
The "Contribution Plan” identifies with departments
only those costs which are incurred directly as a result
of operating that department.
These are the costs which
would not be incurred if the department were discontinued:
clerical salaries, wrapping and other supplies, advertising
and publicity for the department, etc.
When these costs
are deducted from the sales of the department, the dif­
ference represents that department's "contribution" to the
coverage of the fixed overhead costs of the store and the
provision of a net profit.
Just as it was observed pre­
viously that no one unit ever made a profit^ here it might
be observed that no one department in a department store
ever made a profit.
All that a department can do is cover
its direct costs and contribute something to the "pool"
from which a net profit may emerge.
There is hardly a commercial enterprise where the dif­
ferential cost technique would not be of value and Importance.
Another example of its use is in the contracting business,
* Clark, Carlos B., "A Mew Point of View in Respect to
Costs of Operation", Proceedings of the Fifteenth Annual
Convention of the Controllers' Congress of the N.R.D.G.A..
1934.
164
or any other business in which revenue Is secured by means
of sealed bids.
In submitting such bids, a contractor may figure a
total cost of the proposed job— that is, one which includes
an allocation of all fixed costs such as equipment depre­
ciation, executive and administrative salaries, etc.
On
the other hand, he knows that if he has productive facil­
ities standing idle he will be wise to accept the job for
something less than total cost.
He may not calculate the
figure and label it as such, but somewhere in his thinking
he must realize that differential cost must constitute
the lower limit below which his bid must not fall.
Any
bid above differential cost will provide something toward
the coverage of fixed costs which would not otherwise have
been provided.
The upper limit of the bid will be determined largely
by what the contractor thinks his competitor will bid,
and some knowledge of this may be gained by attempting to
determine the competitor's costs.
Mr. Howard Greer dis­
cussed the possibilities of estimating a competitor's costs
and indicated that this technique had real practicability.'1'
If a contractor were aware of his own differential and
total cost and had a good notion as to his competitor's
differential and total costs, he would be in the most
1 Greer, cf. ante., p. 35 (footnote).
16?
favorable position to submit a bid.
Undoubtedly many
contractors have this information in mind, even if it is
not formalized by use of specific terminology and resolved
into written calculations.
Cost accountants can render a
real service to management in all lines of business by
resolving these concepts into formalized calculations
and reports.
The discussion of differential costing should not be
concluded without raising a question as to the effects
of this technique upon the calculation of net Income for
purposes of federal income taxation.
In a manufacturing
concern if all fixed costs are carried directly to the
income statement rather than included in Inventory values,
it is obvious that inventory values are reduced and re­
ported net profits are altered accordingly.
Whether this
method of reporting profits will be accepted by the Com­
missioner of Internal Revenue for tax purposes is doubt­
ful.
The assistant controller of one firm, which is in
the process of installing a differential cost system,
writes that the company’s tax advisors are working on the
matter of whether or not to ask for the Commissioner’s
acceptance of the plan, but so far no decision has been
reached.^
Although the eventual outcome of this matter cannot
1 Private letter, addressed to the author, dated
July 7, 1952.
166
be predicted, certain observations can be made with respect
to the tax aspects of differential costing.
First, even if differential cost valuation of inven­
tories is not acceptable for income tax purposes, there
is no reason why the differential approach cannot be used
for internal reporting purposes and separate inventory
valuations calculated for tax purposes.
referred to above says in this regards
The executive
MWe feel that the
advantages of direct costing for internal purposes are
such that we will definitely use it internally even though
we will make separate calculations for tax purposes.
If
we do make these separate calculations, we will also use
the figures for the valuation of inventory in our pub­
lished financial statements.
We feel that this could be
done with a minimum of extra effort and would provide us
with most of the advantages of direct costing.
However,
our preference is to go the whole way; and we hope that
our tax advisors and public accountants will be able to
1
work out acceptable procedures for doing this.”
It Is further observed that while the differential
costing of manufacturing inventories might reduce reported
Income in the first year that a company adopted the plan,
thereafter there would be no effect upon reported Income
i£ inventories and costs remained the same in each taxable
year.
But usually they do change, and changes in costs
1 Ibid.. Private letter to author, dated July 7, 1952.
and inventories would have the effect of shifting some
expense from one taxable year to another and reported net
profit might thus be reduced in one year; but it would be
offset by a corresponding increase in the following year*
An example will Illustrate this.
Assume that inventories
are unusually large at the close of a particular year.
Under present methods of accounting a portion of the firm's
fixed costs would be carried forward as a part of this
inventory value.
If the inventory were priced at only the
differential cost, all of the fixed factory overhead would
be charged against Income and net profits reduced accord­
ingly.
In the following year however, the situation would
be reversed.
Under present accounting methods the higher
opening Inventory value in the second year would have the
effect of reducing profits in this year, as opposed to the
differential plan where the reduced value of the opening
inventory would cause the net profit to be greater.
Thus
the use of the differential plan might shift profits from
one year to another but in offsetting amounts.
In the first year of adoption of the differential
cost plan, the reported net profit would be reduced be­
cause of the decreased value placed upon the closing in­
ventory.
Even the effect of this might be offset by re­
valuing the opening Inventory in the first year so as to
exclude the fixed factory overhead.
If the amount of the
168
reduction in the opening inventory corresponded with the
amount of the reduction in the ending inventory, there would
be no change in net profit even in the first year, but a
charge would have to be made against retained Income for
the decrease in the value of the opening inventory.
There is one further observation.
The Internal
Revenue Code and the Regulations are not entirely clear
on the treatment of a firm's overhead costs with respect to
inventories.
The Commissioner has always accepted inven­
tory values which Include a proper allocation of overhead
costs such as depreciation, taxes, rent, etc.
On the other
hand, Section 23 of the Code provides for the deduction
of certain expenses— rent, depreciation, taxes, etc.— and
specifically states that these should be deducted in the
year in which incurred.
It would appear, therefore, that
with respect to those items of fixed factory overhead which
are listed in Section 23, full deduction could be made in
the year in which incurred.
This would provide at least a
partial differential costing of inventories.
One of the most Important factors stressed in the
Regulations is that the method used for valuation of inven­
tories should be consistent from year to year.
This fact,
along with the fact that the differential plan would not
greatly alter reported net profits, would lead to the
hope that the Commissioner would grant permission to use
differential costs for inventory values.
At the very
least, it would be hoped that new companies could start
off with it.
170
Conclusions
Many techniques developed In the past several decades
for accounting for fixed costs have been unrealistic from
the standpoint of planning, budgeting and control of a
business enterprise.
They are unrealistic because they
combine fixed and variable costs in one category and then
treat the whole as essentially variable.
They are un­
realistic because they develop cost information in a
manner which does not always conform to the way in which
management thinks.
Spreading of fixed costs to products, territories
and other classifications may have value from a historical
viewpoint as an indication of the long range recovery of
total cost.
But executives who are confronted with keen
competition, and thus have no control over their selling
price, tend to think in terms of differential costs; and
many of the present techniques of accounting for fixed
costs do not provide such information.
In the past, many
methods of accounting were oriented to a long run viewpoint,
whereas many managerial problems require short run analysis.
It was found that firms in the more competitive industries
were turning to differential costs as one factor in the
solution of short run managerial problems.
Cost accounting, for the short run, should recognize
171
from the very outset the basic distinction between variable
costs and fixed costs.
All ensuing cost accounting tech­
niques should be built around this fundamental distinction.
So-called semi-variable costs may be treated as either
variable or fixed depending upon the degree of volume
fluctuations experienced.
A system of differential cost accounting is based
upon this fundamental distinction between fixed and
variable costs; it conforms with management’s concept of
costs and profits, end is founded upon fundamental con­
cepts of economics.
APPENDIX
173
Appendix A
Ten industrial and commercial firms throughout Ohio
were visited during the course of this study.
In these
visits, discussions were held with controllers, treasur­
ers, cost accountants and other company officials regard­
ing many accounting matters, but regarding differential
costs in particular.
Three of the firms were chosen be­
cause it was known that they were interested in differ­
ential costs; the others were chosen in an effort to have
some diversification and on the basis of the cooperation
which was extended.
In each firm an attempt was made to gain some under­
standing of the products and productive operations.
In
many firms extensive tours were made through the plant.
In the three firms which had done some work with differ­
ential costs, their accounting methods were studied in
more detail; and many observations made in these companies
were incorporated in Chapter 5.
In all firms differential
costing was discussed and reactions to this technique
were studied.
Special attention was given to the way in which cost
accounting Information was being used by the various
firms— its role in managerial policy determination and its
relation to price determination.
An effort was made in
each Instance to gain an understanding of the extent of
174
competition which existed in the various companies.
This
was integrated with the price determination policies of
the companies in an effort to understand the role of dif­
ferential costs in price setting.
Much of this material
became the basis for Chapter 3.
Since much of the information obtained from these
plant visits was Incorporated in this dissertation, a
brief abstract is presented herewith of the main points
observed in each firm.
Since much of the information was
of a highly confidential nature, none of the firms will
be identified.
In addition to the firms visited, a wealth of infor­
mation was obtained from visits with Mr. Howard C. Greer,
from his lectures in Accounting 860. Accounting Aspects
of Business Policy Determination at The Ohio State Univer­
sity. and from his writings.
Also from Mr. Greer were
obtained numerous Illustrations of the application of
differential costs, examples of the way in which manage­
ment uses cost information, and ideas on the way in which
prices are determined.
}
175
Company A
This company is located in a town of about 20,000
population and employs between 500 and 600 people in the
manufacture of a coordinated line of small household pro­
ducts.
The products are very high quality; and by the
admission of one company executive, very little competi­
tion exists.
The product is marketed through higher class
department stores, hardware stores and mail-order houses.
Since there is no competing line, the product appears on
store shelves alone.
The executives Interviewed in this company had no
knowledge of differential costing and were reluctant to
see much value in this approach.
cost accounting system
analysis by products.
They had no regular
but semi-annually made a cost
The sole purpose of this analysis
was to provide a means of price setting; and as such, it
appeared Imperative that a full allocation of all fixed
costs be made to products.
The lack of competition for
this company's products was attributed largely to the
careful selling prices which were worked out on the basis
of total cost calculations.
176
Company B
This company Is located in a northern Ohio city and
employs about 350 people In the manufacture of tooth­
brushes.
There are only three major manufacturers of
toothbrushes In the country, but competition is keen among
these.
Each manufactures a number of toothbrushes in
various price ranges, and usually they are marketed in
drugstores where the toothbrushes of each manufacturer
are displayed side by side.
There is just about one tooth­
brush per person sold annually in the United States,and
efforts to increase this ratio have so far been unsuccess­
ful.
Competition is entirely for a share in the existing
market.
The executives of this firm were keenly aware of the
fact that they had little control over selling prices.
When a new style toothbrush was developed, a trial selling
price was stipulated; but several adjustments would usually
be made before a relatively permanent selling price could
be found.
Either the selling price would be altered or the
quality of the brush changed in order to meet competition.
The executive who was interviewed in this company
had a real appreciation for differential costing, although
he had not worked out all of the details of a complete
differential cost system.
The regular costing of units of
production was In terms of total cost on a process basis.
177
However this executive had established a very complete
budgetary system of variable and semi-variable costs for
each department in the plant.
Each semi-variable cost
for each department was budgeted in terms of volume levels.
This budgetary system was useful not only for cost control
purposes, but had been extremely useful in differential
cost studies.
The executive interviewed related a number
of Instances In which differential costing had been the
basis for executive decision.
A number of unusual types of fixed costs were found
in this company.
Because of the small number of firms in
this field, there was no regularly manufactured machinery
for toothbrush-making.
The machines which this firm used
were designed, tooled and built in the company's own
machine shops.
Then in order to provide mechanics to
service and repair these machines, the company had to set
up an extensive mechanic training program.
The cost of
training a mechanic was so great that the firm treated
mechanics' salaries as a fixed expense.
No matter hew
much volume declined, these mechanics were retained for
they could not be replaced if volume Increased again.
This factor had contributed to the firm's realization of
the need for differential costs.
178
Company C
This company is engaged in the manufacture of a light
Industrial machine.
Although there is a considerable amount
of competition in the sale of the machine which this com­
pany manufactures, the company holds patents on a number
of devices which have given it a distinct advantage in the
field.
The basic core of the machine may be manufactured
to stock, but the last stages in the manufacture of the
machine are usually made to customers* specifications.
Since each machine is somewhat different than all
others, a question was raised as to the method by which
selling price was determined.
The answer was 11cost plus”.
When an order was received, a cost estimate was made in
accordance with the particular specifications of that
order.
To this was added a mark-up to arrive at selling
price.
The executive in this firm said that "occasion­
ally** a selling price, so determined, had to be altered
to meet competition, but this was quite infrequent.
The firm used a combination of process and job-order
costs, but both on a total cost basis.
The executives
expressed no knowledge of differential costs and little
interest in the subject.
179
Company D
This company Is an old and mature organization.
It
was the manufacturer of one of the earliest steam-powered
road builders.
In its early history, it also manufactured
farm machinery— tractors, threshers, etc.
In recent years
however this line has been abandoned, and concentration
has centered on diesel and gas-powered road-building
machinery#
The field in which this company is engaged was described
as highly competitive.
There was a minimum of repeat
business, and each sale was usually made only after the
purchaser had carefully considered the products of
competitors#
Being a very old concern this company had reached the
point where many of its buildings had to be abandoned for
heavy manufacturing purposes, making these facilities
available for light manufacturing and storage#
This situation may have been partially responsible
for the fact that the Controller in this company was
keenly aware of the value of the differential cost tech­
nique.
He said that he did not see how any decision was
ever reached without a knowledge of differential costs#
One of the most outstanding features observed in this
company was the fact that it manufactured, with its own
facilities, nearly
every item that went into its completed
product.
partswere purchased from outside firms.
Very few
Accordingly there was a wide diversification of activities
within this plant.
Many different parts are cast in the
foundry and hammered in the forge.
It makes itw own
patterns and molds, welds plate, bores and bends plate,
stamps and presses, makes gears and hydraulic lifts.
In
addition, it makes huge steel and fibre brushes and many
other attachments and accessories for its equipment.
The Controller of this plant recognized that the
decision to manufacture rather than buy these parts was
largely a matter of differential costs.
However he recog­
nised that his present accounting system was inadequate
for differential cost purposes.
This accounting system was essentially a typical total
cost standard system.
Standard costs had been set up for
each department, including such fixed costs as deprecia­
tion, taxes and Insurance.
The Controller had the desire
to eliminate these fixed costs from his standard calcula­
tions, but felt that if he did so the inventory figures
thus calculated would not be accepted by the Commissioner
of Internal Revenue for tax purposes, nor by the company
auditors for published statement purposes.
Furthermore
he felt that he did not have adequate accounting staff to
calculate two cost figures, one including an apportionment
181
of fixed overhead and another excluding fixed overhead.
As a result of these feelings, he had adopted certain
arbitrary procedures which he felt were providing a rough
approximation of differential costs.
Although this was
only a rough calculation, he had developed a ratio
between selling price and this “differential cost” which
served as an important guide to the relative profitability
of products.
182
Company E
This company manufactures a heavy Industrial machine
of great unit value.
The company Is situated 1m a very
small toirn and employs at present about 700 people.
Present operations however are at an extremely high point
of activity— the Controller estimated that they were
operating at about 130# of ftnormal” capacity.
He was quick
to emphasize that this greatly exceeded the point of optimum
efficiency and that total costs rose rapidly at this level
of operation— evidence for the curved cost line.
This Controller emphasized the "feast or famine"
nature of this industry.
Sales in the past four years had
been as followss
194-9
$3 million
1950
$6 million
1951
$9 million
1952 (anticipated)
$12 million
While some of this growth came as a result of plant
expansion, most of it was managed with existing plant
facilities.
In 194-8 the plant was operating at about
60# of capacity, according to the Controller’s estimate.
The effect of competition in this industry is entirely
dependent upon whether they are in the "feast" or "famine"
stage.Prices
are based
years this was done by a
upon cost estimates. For many
cost estimator whomade the
cost
calculations mentally.
More recently he has begun record­
ing his cost calculations in a more formal fashion.
is a total factory cost calculation.
This
Departmental over­
head rates based upon labor are used to allocate fixed
costs to Jobs.
To this cost an attempt is made to add about
35# to cover selling and administrative expenses and a
profit.
Whether or not this 35# mark-up can be maintained
depends upon what stage of the cycle the industry is in.
During the feast stage, the 35# is generally maintained.
During 194-8 (60# capacity), they bid Jobs with mark-ups
as low as 20# over factory cost.
This 20# had not resulted
from any differential cost calculation but resulted merely
from the drive of competition.
Nevertheless the Controller
expressed sincere interest in differential costing and
recognized its value, particularly in periods of "famine".
184
Company F
This firm is the manufacturer of a diversified line
of heavy industrial machinery.
However the product is such
that it wears out rather rapidly, and therefore there is
a considerable “repeat” business and a very extensive
business in the sale of repair parts.
The cost system in this firm was essentially job order
cost, with the use of standards.
In the discussion with
the chief cost accountant there was great emphasis upon
total costs, great emphasis upon “normal capacity" and great
emphasis upon the use of cost information in price setting.
This executive maintained that one of the prime functions
of the cost accounting department was the preparation of
cost information for price determination.
He estimated
that in about 85% of the cases, total cost plus a mark-up
constituted the final selling price.
In the other 15% of
the cases, some adjustment is made in this calculated
selling price "to meet competition.”
At times a “bottom
bid” figure has been calculated, but there are no routine
methods for arriving at this.
In those circumstances where
a “bottom bid” figure was calculated, it amounted essen­
tially to a differential cost calculation.
185
Company G
This was essentially a distributing company employ­
ing about 70 people.
It is a relatively new company which
purchases a common household product in bulk form, packages
it in various size containers, and markets it in grocery
stores throughout the United States.
It is a most highly
competitive product.
The company had practically no system of manufacturing
cost accounting, since its "manufacturing" consists simply
of one packaging operation.
They did have however a
rather highly developed system of distribution cost ac­
counting since their operations were primarily marketing.
The objective of the distribution costing was to arrive
at costs and profits by territories.
A very interesting
system of "sales potentials" had been developed for each
territory, based upon a related, determinable factor in
each district.
At the outset total costs, Including "home
office" expense, had been allocated to territories,
^re
recently this procedure has been abandoned with the
realization that it contributed nothing toward the control
of costs in the territory, and that it contributed nothing
toward an understanding of the profitableness of the
territory.
The only costs now identified by territories are
those actually Incurred in the territorial offices.
This
186
is not strictly a differential cost system, since some home
office expenses may be purely variable with activity in
the territories.
Nevertheless the scheme is an approach
toward a differential cost plan and was initiated in an
effort to gain the advantages of differential costing.
187
Company H
This plant Is a subsidiary of on© of the large glass
corporations and manufactures one product only.
The plant
employs 1,400 people in the routine, mass production of
this one product, although the parent company employs about
25 ,000 .
With production of only one product, the cost account­
ing was relatively simple.
Most direct labor was on a
piece-rate basis, simplifying the control of labor cost.
Breakage amounted to a considerable cost, and this was
reported and controlled on a **pieces broken*1 basis.
A
system of standards was provided which allocated total
factory overhead to products in the usual manner.
Although
no formalized system of differential costs was in use, the
plant*s financial officer had prepared budgets of total
plant operating costs at various levels of output— essen­
tially a flexible budget.
This was a relatively simple pro­
cedure since the plant was tooled to produce only the one
item.
The flexible budget and other cost procedures in this
firm were designed almost entirely for cost control pur­
poses.
setting.
There was no mention of costs in relation to price
When asked about price determination, this execu­
tive was quick to recognize the oligopolistic nature of
188
the glass Industry and the fact that once a price structure
was developed, each firm in the Industry was quite careful
to not disturb it.
The glass item being mass-produced by this firm was
produced by only two other firms in the country.
When the
item was first produced by only one plant, total cost had
probably Influenced price.
When the second and third
firms entered the field, some slight adjustments had been
made in price but nothing drastic.
Since that time the
selling price had remained stable, and it would undoubted­
ly remain stable as long as costs did not change.
The executive was asked whether drastically reduced
demand might bring on price competition.
an emphatic "no".
His answer was
he emphasized that although there were
no eoluslve activities in the glass Industry, the few firms
in the Industry had "learned to live together."
189
Company I
This was a medium-sized department store located in
Columbus, Ohio,
All of the discussion centered around the
two accounting plans outlined in the Standard Expense
Accounting Manual for Department Stores and Specialty
Stores, published by the Controllers' Congress of the
National Retail Dry Goods Association.
This company
used essentially the Net Profit Plan which allocated a
full share of the store fixed overhead cost to each sales
department.
The Controller of the store was only vaguely
familiar with the "Contribution Plan", but the plan was
discussed and compared with the "Net Profit Plan".
The Controller admitted that probably the main reason
for their use of the "Net Profit Plan" was because they
"had always done it that way", and top management was
familiar with this method of reporting.
Although the "Net Profit Plan!' was in use for report­
ing to top management, the Controller did point out that
for purposes of reporting to department managers, a differ­
ent plan was used.
These reports Included sales, cost of
sales and then only two items of expenses clerical salaries
and advertising.
This method of reporting was standard
throughout the store; and although it is not a complete
"Contribution Plan", it is an attempt to achieve
190
essentially the same result:— a department's contribution
to the coverage of the store*s fixed cost and profit.
191
Company J
This was the only firm visited which had what might be
described as a complete differential cost system.
The
system had been installed over a period of about eight
months by G. Charter Harrison, management consultant.
The company manufactures large diesel engines and com­
pressors for industrial uses.
This is another "feast or
famine*' industry; and the need for differential costing
was well outlined by the Controller, not only for special
cost studies but for routine costing as well.
The system first eliminated all fixed costs from
unit production costs and thus eliminated the idle capacity
variances.
This was the first characteristic of the system
which was mentioned by the Controller, with the implication
that it was one of the most Important features.
He stated
that they had, at one time, calculated so-called total cost
figures, but that they had little real meaning.
Everyone
who used the total cost figures with any regularity
developed their own formulas, which they applied to the
total cost to try to reduce it to something meaningful.
After the elimination of fixed overhead, a standard
variable overhead rate was developed by the scattergram
method— plotting total costs at varying levels of output,
then projecting a line which is an average of the plotted
points.
In this particular plant the operations performed
192
on various products were sufficiently similar that one stan­
dard variable expense rate was developed for the entire
plant on a per hour basis.
This standard variable expense rate was not incorpor­
ated in the general ledger accounts.
The latter were
carried at actual amounts, and the actual amounts were
compared with standard by means of
ison.
h
work sheet compar­
The actual was then expressed as a percentage of
standard, providing a ratio analysis of actual perform­
ance.
Thus no variance accounts whatever appeared in the
general ledger.
In addition to providing a standard measure of per­
formance, the standard variable expense rate was used to
determine standard variable costs (differential costs)
of each product, present production as well as proposed,
thus determining each product's contribution to the cover­
age of the firm's fixed costs.
193
Appendix B
NATIONAL ASSOCIATION OF COST ACCOUNTANTS
505 Park Avenue
Telephone
New York 22, N. Y.
Plaza 9-3444
Arthur B. Gunnarson, Secretary
Raymond P. Marple, Assistant Secretary
John L. Doran, Assistant Secretary
July 23, 1951
Mr. Paul L. Noble
The Ohio State University
College of Commerce and Administration
Columbus 10, Ohio
Dear Mr. Nobles
I have your letter of July 17, and I want to congrat­
ulate you on the subject you have selected for your doctor­
al dissertation. It seems to me that we have reached that
stage in the evolution from full allocation costing to
marginal costing where there is a real opportunity for
someone to make a really major contribution to accounting
literature. I hope you will not limit your study to the
utilization of marginal costing for managerial policy
determination, because the job which needs doing is the
application or the marginal approach to all costing,
including inventory valuation and profit measurement.
Perhaps a little of my thinking on this subject may
be of interest to you. It is possible, even probable in
my thinking, that when the history of costing theory is
written some years in the future the concept of normal
capacity and normal burden rates will be pointed to as
the Influence which has been most responsible for retard­
ing the development of cost accounting. By using normal
burden rates fixed costs we converted into variable costs.
Accordingly, during the early development of modern cost
accounting - what I call the first stage or the Inventory
valuation and profit measurement stage - the need for separ­
ate classification and treatment of fixed and variable costs
194
was not appreciated or developed. It was not until we were
well along in the second stage - the cost control stage that the development of flexible budget techniques forced
recognition of the essential difference between fixed and
variable costs. But it is the third stage, which we are
just entering - the cost analysis stage - which has brought
home to a few cost accountants the way in which this essen­
tial difference in the two types of costs can be utilized
to provide better cost information not only for management
policy determination, but for all purposes for which costs
are used.
I am not going to attempt in this letter to give you
a bibliography in marginal costing - I am referring your
letter to Don Mackenzie of the Headquarters staff for that
purpose. However, I would like to outline as briefly as
possible the development in the literature of what is called
"The Direct Cost Plan," because it is through an understend­
ing of this plan that you get an appreciation of how the
marginal approach can be applied to all costing.
In January, 1936, Jonathan Harris of Dewey and Almy
of Boston wrote an article for the N.A.C.A. Bulletin en­
titled "What Did We Earn Last Month" In which he proposed
the elimination of fixed costs from inventory values.
A few issues later we published in the Bulletin a number of
letters from members taking violent exception to Mr.
Harris' proposal. However, the Idea would not die. The
July 1, 1937 Bulletin had an article on the same subject
by Clem N. Kohl, and the idea was discussed at the 1937
conference by Professor Howard Cooper. In the intervening
years several other articles on the subject have appeared,
probably the best of which is the article on "Selling
Overhead to Inventory" by Philip Kramer In the Bulletin
for January 15» 1947In the meantime the idea had been developed independ­
ently in England and was presented in an article in a 1940
issue of the English "Cost Accountant." As in this cohntry,
this first article was followed by a number of letters to
the editor disagreeing with the idea. However, the concept
has apparently taken hold faster in England than in this
country and visiting accountants from England are surprised
that so little has been done with marginal costing in
this country. A book entitled "Marginal Costing" by
Lawrence and Humphreys was published in England in 1947*
195
Recently at the N.A.C.A. Annual Conference in Chicago,
Charles Headlee, Controller of Westinghouse made some com­
ments on the direct cost plan, which is marginal costing
applied to inventory valuation, which helps to bring this
story up to.date. The two pages from his talk which bear
on this matter are enclosed.
Perhaps it was the discussions in the N.A.C.A. Com­
mittee on Research regarding the contributions vs. the
full allocation approach to the treatment of nonmanufacturing
costs which cause me to realize the possibilities in the
application of the marginal cost approach to all purposes
for which costs are used. You will find considerable
bearing on this matter in the report Issued May, 1951*
under the title "Assignment of Non-Manufacturing Costs
for Managerial Decisions."
This letter is too long. Mr. Mackenzie will write
you as to specific references. Should you be in New York
in the near future, I would enjoy discussing this subject
with you.
With kindest regards,
Very truly yours,
/s/
Ray Marple
Assistant Secretary
Technical Service
RPM: ja
196
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Autobi ography
I, Paul LeMoyne Noble, was born in Cleveland, Ohio,
October 29, 1921.
I received my secondary school educa­
tion in the public schools of the city of Cleveland, Ohio*
My tindergraduate training was obtained at The Ohio Univer­
sity, Athens, Ohio, from which I received the degree
Bachelor of Science in Commerce in 1942.
I completed
an advanced course in Personnel Psychology at The Univer­
sity of California in 1943 as a part of the Army Special­
ized Training Program.
From The Ohio State University,
I received the degree Master of Business Administration
in.1949*
I became a Certified Public Accountant in the
State of Ohio in 1950.
I was appointed a Graduate Assist­
ant in the Department of Accounting at The Ohio State
University in January, 1947, and Instructor in Accounting
in October, 1947.
I held this latter position while com­
pleting the requirements for the degree Doctor of Philos­
ophy*